THE PROBLEMS AND PROMISE OF ENTREPRENEURIALPARTNERSHIPS: DECISION-MAKING,OVERCONFIDENCE, AND LEARNING INFOUNDING TEAMS

创业伙伴关系的问题与前景：决策制定、过度自信以及学习型团队的信息不足

JOHN S. CHEN University of Florida 陈约翰 S. 佛罗里达大学

DANIEL W. ELFENBEIN Washington University in St. Louis 丹尼尔·W·埃尔芬贝恩 圣路易斯华盛顿大学

HART E. POSEN University of WisconsinMadison HART E. POSEN 威斯康星大学麦迪逊分校

MING ZHU WANG Washington University in St. Louis MING ZHU WANG 圣路易斯华盛顿大学

How should decision-making be organized in entrepreneurial teams when founders exhibit confidence biases? New ventures are commonly founded by teams of entrepreneurs, who must employ a decision-making structure that implicitly or explicitly defines how individual beliefs are aggregated into team decisions. We consider this issue through the lens of organizational economics, which focuses on decision-making governance. Using a computational model, we consider three archetypal decision-making structures: partnership voting, a boss with employees, and a buyout option (partnership convertible to boss structure). We highlight the conditions under which partnership voting is an effective means of governing market entry and exit decisions when teams’ decision-making is informed by efforts to learn about the merits of uncertain opportunities. The promise of partnership voting is realized when entrepreneurs are either unbiased or optimistic about their likelihood of success. Partnership voting is problematic when entrepreneurs differ in their biases or respond too rapidly to new information, in which case a buyout option is better. From a policy perspective, we show that confidence biases may be managed by selectively matching the decision-making structure to entrepreneurs’ biases, and that doing so may substantially improve the performance of new ventures. 当创业者表现出信心偏差时，创业团队的决策应该如何组织？新企业通常由创业团队创立，这些团队必须采用一种决策结构，该结构隐含或明确地定义了如何将个人信念汇总为团队决策。我们从组织经济学的角度来考虑这个问题，该角度关注决策治理。通过计算模型，我们考虑了三种典型的决策结构：合伙投票、上级与员工制，以及买断选择权（合伙制可转换为上级制）。我们强调，当团队的决策是基于努力了解不确定机会的价值时，合伙投票是治理市场进出决策的有效手段。当创业者对自己的成功可能性无偏或乐观时，合伙投票的优势得以实现。当创业者的偏差不同或对新信息反应过快时，合伙投票就会出现问题，在这种情况下，买断选择权会更好。从政策角度来看，我们表明，通过有选择地将决策结构与创业者的偏差相匹配，可以管理信心偏差，而这样做可能会显著提高新企业的绩效。

When a new venture is founded by a team of entrepreneurs, how should they organize decision-making? A founding team must employ a decision-making structure that implicitly or explicitly defines how individuals’ beliefs about, for instance, market entry and exit are aggregated into team decisions. Should the founders be voting partners, jointly responsible for critical decisions, or should one of the founders be the boss? How should the decision-making structure change when the founders exhibit confidence biases? Although it has long been known that new ventures are frequently founded by teams (e.g., Cooper, Woo, & Dunkelberg, 1989), the question of how decision-making should be organized remains largely unaddressed in the extant literature, which has instead focused on issues such as team formation, composition, and affect.1 To shed light on these issues, we view founding teams through the lens of organizational economics, which focuses on the design of decision-making governance (e.g., Klein, Mahoney, McGahan, & Pitelis, 2019). We examine the conditions under which partnership voting is an effective means of governing market entry and exit decisions when entrepreneurs exhibit confidence biases. Our key insight is that the structure of decisionmaking must follow from the characteristics of entrepreneurs’ biases. The promise of partnership voting is realized when entrepreneurs are optimistic about their likelihood of success, but partnership voting is problematic when entrepreneurs differ in their biases or update their beliefs too rapidly in response to new information. 当一个新企业由创业团队创立时，他们应该如何组织决策？创始团队必须采用一种决策结构，该结构会隐含或明确地定义个体对市场进入和退出等问题的看法如何汇总为团队决策。创始人应该是投票伙伴，共同对关键决策负责，还是应该有一位创始人担任老板？当创始人存在信心偏差时，决策结构应如何调整？虽然长期以来人们都知道新企业经常由团队创立（例如，Cooper, Woo, & Dunkelberg, 1989），但关于决策应如何组织的问题在现有文献中仍未得到充分探讨，而现有文献更多关注团队组建、构成和情感等问题。1 为了阐明这些问题，我们从组织经济学的角度审视创始团队，该领域关注决策治理的设计（例如，Klein, Mahoney, McGahan, & Pitelis, 2019）。我们研究在创业者存在信心偏差时，伙伴投票作为管理市场进入和退出决策的有效手段的适用条件。我们的核心见解是，决策结构必须由创业者偏差的特征决定。当创业者对自身成功可能性持乐观态度时，伙伴投票的优势得以体现；但当创业者的偏差存在差异，或对新信息的信念更新过于迅速时，伙伴投票则存在问题。

In the popular imagination, entrepreneurial teams are often viewed as decision-making partnerships. Familiar examples include Gates and Allen at Microsoft or Jobs and Wozniak at Apple. Entrepreneurial opportunities are highly uncertain “unique business investments for which it is difficult … to assign meaningful probabilities to outcomes … [therefore] individuals will reach different decisions, even if they share the same objectives” (Foss & Klein, 2012: 78), and failure is highly likely (Kerr & Nanda, 2010; Knott & Posen, 2005). In many cases, the decisions that arise from two heads may be better than those arising from just one. Recent empirical evidence, however, suggests that partnership decision-making may be less common than we might expect.2 Data from a nationally representative survey of the U.S. population found that only $1 8 %$ of new firms are governed by equity partnerships (Lee, 2020), and firms with two to four owners represent a mere $3 3 %$ of all private businesses in operation for two years or less (United States Census Bureau, 2016). This may be explained, in part, by the fact that partnerships can be difficult to manage and sustain for a variety of interpersonal reasons (Klotz et al., 2014). As we argue in this paper, it might also be the case that the governance of entrepreneurial decision-making is not always effectively managed by a pure partnership decision-making structure. Indeed, while we may think of partnership voting as the default structure, the relative paucity of partnerships suggests that there are costs of partnerships that are not fully understood. 在大众的想象中，创业团队常被视为决策伙伴关系。人们熟悉的例子包括微软的盖茨和艾伦，或苹果的乔布斯与沃兹尼亚克。创业机会是高度不确定的“独特商业投资，难以……为结果分配有意义的概率……[因此]即使目标相同，个人也会做出不同决策”（Foss & Klein，2012：78），且失败的可能性极高（Kerr & Nanda，2010；Knott & Posen，2005）。在许多情况下，两人共同决策可能优于个人单独决策。然而，最近的实证研究表明，伙伴关系决策可能比我们预期的更为少见。2 美国人口全国代表性调查的数据显示，仅有 18% 的新企业由股权合伙制管理（Lee，2020），且拥有 2 至 4 名所有者的企业仅占所有运营时间不足两年的私营企业的 33%（美国人口普查局，2016）。部分原因可能是合伙制由于多种人际原因难以管理和维持（Klotz 等人，2014）。正如我们在本文中所论证的，创业决策的治理也可能并非总是由纯粹的合伙制决策结构有效管理。事实上，尽管我们可能将合伙制投票视为默认结构，但合伙制的相对稀缺性表明，合伙制存在一些尚未被充分理解的成本。

To advance our understanding of how alternative decision-making structures impact critical decisions such as entry and exit and the performance of founding teams, we must account for the defining features of entrepreneurship. These features include the existence of substantial uncertainty about the merits of opportunities, the need to learn about opportunities by gathering additional information, and the presence of behavioral biases that hamper learning and decision-making. We develop a computational model that builds on the entrepreneurial learning framework of Chen, Croson, Elfenbein, and Posen (2018), which conceptualized entrepreneurship as an unfolding feedback-learning process through which teams discover the viability of their opportunities and make market entry and exit decisions. In our model, a two-person team is endowed with an entrepreneurial idea of uncertain merit. Each team member is essential to implementing the idea, in the sense that each supplies unique human capital that is critical for operating the business. At all times, these agents maximize their individual profits conditional on their beliefs, but their beliefs may be inaccurate due to bias. Entry into the marketplace is costly for both individuals, so, prior to making an entry decision and investing substantial resources, they seek to learn more about the merits of the opportunity (e.g., engaging focus groups or developing a prototype). This feedback is subject to uncertainties that make learning difficult, and each entrepreneur may interpret the feedback somewhat differently. At the end of this pre-entry learning period, the team must decide whether to enter the market. If they do choose to enter, they will continue to learn about their opportunity through the profits and losses their firm accrues, and, if they come to conclude that they entered erroneously, they may decide to exit. 为了深入理解替代决策结构如何影响进入和退出等关键决策以及创始团队的表现，我们必须考虑创业的核心特征。这些特征包括：对机会价值存在重大不确定性、需要通过收集更多信息来了解机会，以及存在阻碍学习和决策的行为偏差。我们构建了一个计算模型，该模型基于Chen、Croson、Elfenbein和Posen（2018）的创业学习框架，该框架将创业概念化为一个不断展开的反馈学习过程，团队通过这一过程发现其机会的可行性并做出市场进入和退出决策。在我们的模型中，一个两人团队拥有一个价值不确定的创业想法。每个团队成员都必须执行该想法的实施，因为每个人都提供了对企业运营至关重要的独特人力资本。在任何时候，这些主体都会在其信念的条件下最大化个人利润，但由于偏差，他们的信念可能不准确。进入市场对个人而言都是有成本的，因此在做出进入决策并投入大量资源之前，他们会寻求更多地了解机会的价值（例如，开展焦点小组讨论或开发原型）。这种反馈存在不确定性，使得学习变得困难，每个创业者可能会对反馈有不同的解读。在进入前的学习期结束时，团队必须决定是否进入市场。如果他们选择进入，他们将通过企业产生的利润和亏损继续了解其机会，如果他们得出自己进入错误的结论，可能会决定退出。

We consider three archetypal and practically grounded decision-making structures for founding teams of two individuals. These structures correspond to the classic decision-making structures examined in Sah and Stiglitz’s (1985, 1986) theory of economic organization and recent extensions of this theory in the management literature (Christensen & Knudsen, 2010; Csaszar, 2013; Csaszar & Eggers, 2013). First, a partnership voting structure is the case in which both team members split post-entry returns and must agree on entry and continuation decisions. Second, a boss-employee arrangement is the case in which a single agent—that is, the boss— has full decision rights. Third, a buyout option is the case in which the pair begins learning about the opportunity as an equal partnership. If both individuals agree about entering the market, the structure remains a partnership post-entry, but, if there is disagreement, a pro-entry entrepreneur may buy out the other individual, such that the governance structure changes to a boss-employee arrangement post-entry. 我们考虑了两种个体创始团队的三种典型且基于实践的决策结构。这些结构对应于Sah和Stiglitz（1985、1986）的经济组织理论中研究的经典决策结构，以及该理论在管理文献中的最新扩展（Christensen & Knudsen, 2010；Csaszar, 2013；Csaszar & Eggers, 2013）。首先，合伙投票结构是指团队成员共同分配进入后的收益，并且必须就进入和持续经营决策达成一致。其次，老板-员工安排是指单个代理人（即老板）拥有全部决策权。第三，买断选择权是指两人以平等合伙的方式开始了解该机会。如果两人都同意进入市场，该结构在进入后仍为合伙制；但如果存在分歧，支持进入的创业者可以买断另一方，从而在进入后将治理结构转变为老板-员工安排。

Our central concern is how confidence biases moderate the effectiveness of alternative team decision-making structures. A critical challenge in investigating the learning process of entrepreneurs is that they can be subject to decision-making biases such as overconfidence (Åstebro, Herz, Nanda, & Weber, 2014; Cain, Moore, & Haran, 2015; Chen et al., 2018; Wu & Knott, 2006). These biases may underlie common mistakes such as excess entry into the market (Camerer & Lovallo, 1999; Koellinger, Minniti, & Schade, 2007) and delayed exit from the market when a new venture’s prospects are poor (Åstebro, Jeffrey, & Adomdza, 2007; DeTienne, Shepherd, & De Castro, 2008; Elfenbein, Knott, & Croson, 2017; Gimeno, Folta, Cooper, & Woo, 1997). In particular, we follow Moore and Healy (2008) in examining both “estimation bias” (overly optimistic or pessimistic beliefs) and “precision bias” (over- or under-responsiveness of individuals’ beliefs to new information). 我们的核心关注点是信心偏差如何调节替代团队决策结构的有效性。研究企业家学习过程的一个关键挑战在于，他们可能会受到过度自信等决策偏差的影响（Åstebro, Herz, Nanda, & Weber, 2014；Cain, Moore, & Haran, 2015；Chen et al., 2018；Wu & Knott, 2006）。这些偏差可能是市场过度进入（Camerer & Lovallo, 1999；Koellinger, Minniti, & Schade, 2007）以及新企业前景不佳时延迟退出市场（Åstebro, Jeffrey, & Adomdza, 2007；DeTienne, Shepherd, & De Castro, 2008；Elfenbein, Knott, & Croson, 2017；Gimeno, Folta, Cooper, & Woo, 1997）等常见错误的根源。特别是，我们遵循Moore和Healy（2008）的研究，考察“估计偏差”（过度乐观或悲观的信念）和“精确性偏差”（个人信念对新信息的反应过度或不足）。

A core insight from our model is that confidence biases may be managed by selectively matching the decision-making structure to the biases of the entrepreneurs involved in the venture. Traditional policies for mitigating bias are based on screening out the most biased individuals (e.g., Elfenbein et al., 2017; Gutierrez, Åstebro, & Obloj, 2020), de-biasing them via education (e.g., Elfenbein & Knott, 2015; Lovallo & Sibony, 2010; Shane, 2008; Shepherd & Patzelt, 2017), or structuring the processes through which they learn (Camuffo, Cordova, Gambardella, & Spina, 2020). Our model suggests a complementary approach: selecting the decision-making structure that most effectively ameliorates the consequences of bias and identifies the structures that perform best when the potential biases of entrepreneurs are known (e.g., via diagnostic testing) or when only the population distribution of biases is known. 我们模型的一个核心见解是，通过有选择地将决策结构与创业企业中涉及的创业者的偏见相匹配，可以管理信心偏见。缓解偏见的传统政策包括筛选出最有偏见的个人（例如，Elfenbein等人，2017年；Gutierrez、Åstebro和Obloj，2020年），通过教育使他们去偏见（例如，Elfenbein和Knott，2015年；Lovallo和Sibony，2010年；Shane，2008年；Shepherd和Patzelt，2017年），或者构建他们学习的流程（Camuffo、Cordova、Gambardella和Spina，2020年）。我们的模型提出了一种补充方法：选择最有效地减轻偏见后果的决策结构，并识别在已知创业者潜在偏见（例如，通过诊断测试）或仅知道偏见的总体分布时表现最佳的结构。

We highlight three results related to the promise and problems of a partnership decision-making structure relative to the boss-employee or buyout option arrangements. First, when prospective entrepreneurs are unbiased, the partnership structure, in which both founders must agree on both entry and continuation decisions, yields better results than the alternative decisionmaking structures. With unbiased team members, partnership effectively balances errors of omission and commission in entry and exit decisions. Teams of unbiased agents with high-quality opportunities fail to enter the market at a moderate rate under a partnership, while those with low-quality opportunities are much less likely to enter than with alternative structures. Additionally, when an unbiased team with a low-quality opportunity mistakenly enters, the partnership structure leads to more rapid exit. 我们重点关注了与伙伴关系决策结构（相对于老板-员工或收购选择权安排）的前景和问题相关的三个结果。首先，当潜在创业者不偏不倚时，伙伴关系结构（其中两位创始人必须就进入和延续决策达成一致）比其他决策结构产生更好的结果。在团队成员不偏不倚的情况下，伙伴关系能有效平衡进入和退出决策中的遗漏和失误。拥有高质量机会但成员不偏不倚的团队，在伙伴关系结构下进入市场的速度适中，而拥有低质量机会的团队进入市场的可能性比其他结构下要低得多。此外，当一个不偏不倚的团队因低质量机会而错误进入时，伙伴关系结构会导致更快的退出。

Second, when prospective entrepreneurs come from populations with a distribution of “neutral” biases (i.e., individuals are unbiased on average, although each individual may be biased), the buyout option structure provides better results than does partnership. The strength of the buyout option in this case is that it enables a team to overcome the problem of a single pessimistic partner who can unilaterally veto entry, leading to fewer “failures to enter” for teams with high-quality opportunities. This “mistaken nonentry” results in irreversible foregone gains, while entry mistakes by teams with low-quality opportunities, the vulnerability of the buyout option, can still be mitigated via exit. When we relax the assumption of neutral biases, however, the relative effectiveness of alternative structures changes: partnership generates greater returns in a population of optimists, as its structure reduces entry of low-quality enterprises (that individual optimists would launch). Furthermore, the length of time allotted for pre-entry learning can change the rank order of the efficacy of these decision-making structures. For instance, when potential entrepreneurs are, on average, optimistic about the quality of their opportunities, buyout can be the best structure when the pre-entry learning period is short. Yet, for longer learning periods, partnership is best, and boss-employee also outperforms the buyout option. Taken together, these first two insights show the contingent nature of commitment (partnerships) and flexibility (buyout option) among possibly biased entrepreneurial teams. 其次，当潜在创业者来自具有“中性”偏见分布的群体（即个体平均而言无偏见，尽管每个个体可能存在偏见）时，买断选择权结构比合伙制能带来更好的结果。在这种情况下，买断选择权的优势在于它能让团队克服单个悲观合伙人可能单方面否决进入的问题，从而使拥有高质量机会的团队减少“未能进入”的情况。这种“错误的不进入”会导致不可逆转的既得收益损失，而对于低质量机会的团队而言，其进入错误可以通过退出机制得到缓解。然而，当我们放松中性偏见的假设时，替代结构的相对有效性会发生变化：在乐观主义者群体中，合伙制能产生更大的回报，因为其结构减少了低质量企业（即个体乐观主义者会发起的企业）的进入。此外，分配给进入前学习的时间长度也会改变这些决策结构效力的排名顺序。例如，当潜在创业者平均对其机会的质量持乐观态度时，若进入前学习期较短，买断制可能是最佳结构。然而，随着学习期延长，合伙制成为最佳选择，且“老板-员工”结构也会优于买断制。综合来看，这两个初步见解表明，在可能存在偏见的创业团队中，承诺（合伙制）和灵活性（买断选择权）的有效性具有情境依赖性。

Finally, decision-making structures impact the dynamics of entry and exit patterns. When entrepreneurs are drawn from a population characterized by a distribution of biases, the decision-making structures shape both the types of biases exhibited by firms that choose to enter the market and entrants’ performance. The partnership structure may appear to be more successful from the perspective of an econometrician who can only observe firms that have elected to enter the market, even when the buyout structure is superior in expectation (i.e., at the start of the learning process). Furthermore, the model predicts that firms with partnership structures will be less likely to enter, so they will be underrepresented among entrants relative to their frequency among the set of teams that start learning about an opportunity. This observation, along with the other problems related to partnership outlined above, suggests a potential explanation for the paucity of partnerships. Moreover, our model yields testable predictions that boss-employee founders will exhibit both greater overestimation and overprecision biases than founders in partnerships, and that both estimation and precision biases in partnerships will be positively correlated among founders. 最后，决策结构会影响进入和退出模式的动态。当创业者来自一个以偏见分布为特征的群体时，决策结构会塑造选择进入市场的企业所表现出的偏见类型以及进入者的绩效。从只能观察到选择进入市场的企业的计量经济学家的角度来看，合伙制结构可能显得更成功，即使收购结构在预期中更优（即在学习过程开始时）。此外，该模型预测，采用合伙制结构的企业进入的可能性更低，因此相对于在开始关注机会的团队中所占的频率，它们在进入者中的代表性不足。这一观察结果，以及上述与合伙制相关的其他问题，为合伙制的稀缺性提供了一个潜在解释。此外，我们的模型得出了可检验的预测，即老板-员工型创始人将比合伙制创始人表现出更大的高估和过度精确性偏差，并且合伙制中创始人的估计偏差和精确性偏差之间将呈正相关。

THEORETICAL BACKGROUND

理论背景

Scholars of entrepreneurship increasingly recognize that new ventures are often founded by teams rather than lone entrepreneurs (Klotz et al., 2014). Beckman (2006), for example, constructed a sample of 173 high-tech firms in Silicon Valley founded between 1982 and 1995, and discovered that only 18 had been launched by solo entrepreneurs. Foss, Klein, Kor, and Mahoney (2008: 74) focused their inquiry on entrepreneurial judgment, which is necessarily “influenced by the composition and .. dynamics of the entrepreneurial management team.’ .“3 Taking a “team perspective,” then, is critical to deepening our knowledge of entrepreneurial dynamics. 创业学者越来越认识到，新企业往往由团队而非个体创业者创立（Klotz等人，2014）。例如，Beckman（2006）构建了1982年至1995年间在硅谷成立的173家高科技企业样本，发现其中仅有18家是由个体创业者发起的。Foss、Klein、Kor和Mahoney（2008：74）的研究聚焦于创业判断，而创业判断“必然受到创业管理团队的构成和……动态的影响”。3因此，从“团队视角”出发对于深化我们对创业动态的认识至关重要。

Once entrepreneurial endeavors are conceptualized as team (rather than individual) pursuits, several new and distinct theoretical questions emerge. For example, how do entrepreneurial teams form? Do different formation processes lead to systematic differences in team composition (e.g., Agarwal, Campbell, Franco, & Ganco, 2016; Aldrich & Kim, 2007)? Does similarity between team members— whether demographic, experience related, or in social ties—enhance or reduce new venture performance (e.g., Ganco, Campbell, & Raffiee, 2016; Zenger & Lawrence, 1989)? Similarity between team members may facilitate communication and execution, but at the expense of searching for novel solutions (e.g., Beckman, 2006; West, 2007); it may also reflect redundant external networks (e.g., Beckman, Burton, & O’Reilly, 2007). Another important question arises regarding performance: do solo-founded firms outperform team-founded ones? Greenberg and Mollick (2018), for example, found that solo ventures involved in crowdfunding last longer than team-founded ones; however, as much literature on persistence in entrepreneurship suggests, survival does not necessarily equate with success. 一旦创业活动被概念化为团队（而非个人）的追求，就会出现几个新的、不同的理论问题。例如，创业团队是如何形成的？不同的形成过程是否会导致团队构成的系统性差异（例如，Agarwal, Campbell, Franco, & Ganco, 2016；Aldrich & Kim, 2007）？团队成员之间的相似性——无论是人口统计学特征、经验相关还是社会关系方面——是会提高还是降低新企业的绩效（例如，Ganco, Campbell, & Raffiee, 2016；Zenger & Lawrence, 1989）？团队成员之间的相似性可能促进沟通和执行，但会以牺牲寻找新颖解决方案为代价（例如，Beckman, 2006；West, 2007）；它也可能反映冗余的外部网络（例如，Beckman, Burton, & O’Reilly, 2007）。关于绩效，还有一个重要问题：个人创立的公司是否比团队创立的公司表现更好？例如，Greenberg和Mollick（2018）发现，参与众筹的个人创业项目比团队创立的项目持续时间更长；然而，正如许多关于创业持续性的文献所表明的那样，生存并不一定等同于成功。

While previous work has contributed greatly to our understanding of how founding team characteristics and size relate to entrepreneurial performance, it has not examined what we believe to be a critical feature of entrepreneurial teams: the structure of decisionmaking inside the organization. Given the empirical nature of much prior research, this is not wholly surprising, as decision rights are not systematically reported by organizations. We assert that theory related to the structure of decision-making is particularly valuable in this setting given the paucity of reported data about these structures, both at a nascent (pre-entry) phase and subsequent to entry. Conceptually, decision-making can be concentrated in the hands of a few (or one) or it can be more decentralized through the use of a voting rule that demands, for example, plurality or consensus. These different decision-making structures aggregate individuals’ heterogeneous information, and potentially conflicting objectives, differently. As we argue below, the process through which information is aggregated and decisions are made critically impacts how team characteristics translate into organizational performance. 虽然先前的研究极大地帮助我们理解了创始团队的特征和规模与创业绩效之间的关系，但它并未考察我们认为创业团队的一个关键特征：组织内部的决策结构。考虑到许多先前研究的实证性质，这并不完全令人惊讶，因为组织并未系统地报告决策权。我们认为，鉴于在初创（进入前）阶段以及进入之后，关于这些结构的报告数据都很匮乏，与决策结构相关的理论在这种情况下特别有价值。从概念上讲，决策可以集中在少数人（或一个人）手中，也可以通过使用要求（例如，多数或共识）的投票规则实现更分散的决策。这些不同的决策结构以不同方式汇总个体的异质信息和潜在的冲突目标。正如我们在下文所论证的，信息汇总和决策制定的过程会严重影响团队特征如何转化为组织绩效。

Entrepreneurial Decision-Making Structures and Learning

创业决策结构与学习

While entrepreneurship scholars have not extensively examined the decision-making structures of new ventures, scholars of organizations have long been interested in team decision-making, and, in particular, in how organizational decision-making structures shape the properties of decisions. Underlying this view is the classical conception of the organization as an information processing system (Galbraith, 1974; March & Simon, 1958). Indeed, for Simon (1947/1997: 19), information processing is the basis for the existence of the organization, reflecting “the pattern of communications and relations among a group of human beings, including the processes for making and implementing decisions.” More recently, there has been renewed interest in the aggregation of distributed information into a single organization-level decision, due to the popularity of concepts such as the wisdom of crowds (e.g., Page, 2008). 虽然创业学者尚未广泛研究新企业的决策结构，但组织学者长期以来一直对团队决策感兴趣，特别是组织决策结构如何塑造决策的特性。这种观点的基础是将组织视为信息处理系统的经典概念（Galbraith，1974；March & Simon，1958）。事实上，对于Simon（1947/1997：19）而言，信息处理是组织存在的基础，反映了“一群人之间的沟通和关系模式，包括制定和实施决策的过程”。近年来，由于“群体智慧”等概念的流行（例如Page，2008），人们对将分散信息聚合为单一组织层面的决策重新产生了兴趣。

A salient question in the organizational context is “how does organizational design affect decisionmaking?” (Christensen & Knudsen, 2010: 71). Sah and Stiglitz (1985, 1986) developed a formal treatment of decision screening in organizations. In their model, individuals may be organized into different decision-making structures. A project is revealed to the organization, and a decision is made to accept or reject the project based on rules of the particular decision-making structure that aggregates individuals’ “screening functions” (individuals’ beliefs about the merits of the project) into an organizational decision. Sah and Stiglitz (1985, 1986) explicitly contrasted hierarchies with polyarchies, which are related to “AND” and “OR” logical functions. The objective in this model is to balance errors of commission against errors of omission in a manner that maximizes performance. Christensen and Knudsen (2010) extended this model to the full range of organizational structures between hierarchy and polyarchy. Csaszar and Eggers (2013) examined the optimal choice of structure, given properties of the external environment and knowledge of individuals. Piezunka, Aggarwal, and Posen (2020) extended the model to include individual learning. 在组织情境中，一个突出的问题是“组织设计如何影响决策？”（Christensen & Knudsen，2010：71）。Sah和Stiglitz（1985，1986）对组织中的决策筛选进行了正式的处理。在他们的模型中，个体可能被组织成不同的决策结构。一个项目被提交给组织，然后根据特定决策结构的规则（该结构将个体的“筛选功能”，即个体对项目价值的判断，整合为组织决策）来决定接受或拒绝该项目。Sah和Stiglitz（1985，1986）明确对比了层级制（hierarchies）和多元制（polyarchies），这两者分别与“与”（AND）和“或”（OR）逻辑函数相关。该模型的目标是在平衡“错误执行”与“错误遗漏”的同时，最大化组织绩效。Christensen和Knudsen（2010）将这一模型扩展到层级制与多元制之间的所有组织结构。Csaszar和Eggers（2013）考察了在外部环境特性和个体知识已知的情况下，结构的最优选择。Piezunka、Aggarwal和Posen（2020）则将该模型扩展到包含个体学习的情况。

Applying the logic of the Sah and Stiglitz (1985, 1986) model to issues of entrepreneurship requires further articulation of the theory to account for the process of learning about an opportunity that precedes decision-making. The Sah and Stiglitz (1985, 1986) model focuses on one-shot, or independent, screening decisions in which there is no individual learning about the merits of the alternatives being screened. With the exception of recent work by Piezunka et al. (2020), the literature building on Sah and Stiglitz (1985, 1986) has not considered the role of ongoing feedback in shaping team-level outcomes. 将Sah和Stiglitz（1985，1986）模型的逻辑应用于创业问题，需要进一步阐述该理论，以解释决策前关于机会的学习过程。Sah和Stiglitz（1985，1986）模型侧重于一次性或独立的筛选决策，在此过程中，个体不会对被筛选的备选方案的优劣进行学习。除了Piezunka等人（2020）的近期研究外，基于Sah和Stiglitz（1985，1986）模型的文献尚未考虑持续反馈在塑造团队层面结果中的作用。

Yet, as we think of it, learning is fundamental to entrepreneurship. Entrepreneurs engage in a process of learning over time about the merits of an opportunity because such opportunities are often highly uncertain (e.g., Foss & Klein, 2012; Kerr, Nanda, & Rhodes-Kropf, 2014; Knight, 1921; Packard, Clark, & Klein, 2017; Wu & Knott, 2006), and each entrepreneur may interpret the feedback somewhat differently (Foss & Klein, 2012). The importance of learning has been increasingly recognized in the literature (e.g., Minniti & Bygrave, 2001; Woo, Daellenbach, & Nicholls-Nixon, 1994), although, as Cope (2005: 373) noted, “in terms of theory building, many aspects of entrepreneurial learning remain poorly understood.” Extant research on entrepreneurial learning can be classified on the basis of whether learning occurs pre-entry (e.g., Elfenbein et al., 2010; Moeen & Agarwal, 2017; Wu & Knott, 2006) or post-entry (e.g., Frank, 1988; Jovanovic, 1982; Parker, 然而，当我们思考时，学习对于创业至关重要。创业者会随着时间推移，在学习关于机会价值的过程中不断探索，因为这类机会往往具有高度不确定性（例如Foss & Klein, 2012；Kerr, Nanda, & Rhodes-Kropf, 2014；Knight, 1921；Packard, Clark, & Klein, 2017；Wu & Knott, 2006），并且每位创业者可能对反馈的解读有所不同（Foss & Klein, 2012）。学习的重要性在文献中已得到越来越多的认可（例如Minniti & Bygrave, 2001；Woo, Daellenbach, & Nicholls-Nixon, 1994），尽管正如Cope（2005: 373）所指出的，“就理论构建而言，创业学习的许多方面仍然知之甚少。” 现有的创业学习研究可以根据学习发生在进入前（例如Elfenbein et al., 2010；Moeen & Agarwal, 2017；Wu & Knott, 2006）还是进入后（例如Frank, 1988；Jovanovic, 1982；Parker,

2006). Thus, the learning process starts prior to the market entry decision. Before substantial entry costs are incurred, be they opportunity or financial costs, entrepreneurs gather data about the merits of the opportunity. This learning underpins the critical entry/termination decision. If the decision is made to pay the cost to enter the market, learning continues as market-based feedback (profits and losses) is ongoing and exit/continuation decisions are made repeatedly over time. The process of learning integrates the pre- and post-entry periods because what is learned pre-entry influences both which firms enter and their decisions post-entry (Chen et al., 2018). 2006年）。因此，学习过程在市场进入决策之前就已经开始。在产生实质性的进入成本（无论是机会成本还是财务成本）之前，企业家会收集有关该机会价值的数据。这种学习是关键的进入/退出决策的基础。如果决定支付成本进入市场，学习过程会随着基于市场的反馈（利润和亏损）的持续存在而持续进行，并且退出/继续经营的决策会随着时间反复做出。学习过程将进入前和进入后阶段整合起来，因为进入前学到的内容会影响哪些企业进入市场以及它们在进入后的决策（Chen等人，2018）。

The discussion of learning above is silent on how decisions are made when the new venture is founded by a team of entrepreneurs. Consider an entrepreneurial team consisting of two individuals who learn about the merits of an opportunity from independent sources pre- and post-entry. At the time when entry/termination and exit/continuation decisions are made, the theoretical logic outlined by Sah and Stiglitz (1986) suggests a conceptually simple mapping to three ideal types of decision-making structures in entrepreneurial ventures. First, an equal partnership voting structure has characteristics of hierarchy as outlined in Sah and Stiglitz (1986), as both entrepreneurs must agree to enter the market and, post-entry, they must both agree to remain in the market (i.e., not exit). In contrast, the boss-employee structure gives one individual fiat in decision-making. Intermediate to these two functions is a buyout option structure. The buyout option structure starts with a partnership but can convert to a boss-employee structure at the time of the entry decision. If team members disagree on the merits of an opportunity, the positively inclined entrepreneur buys out the negatively inclined entrepreneur by paying them at least their opportunity costs, effectively hiring them as an employee, and, in doing so, assumes full decision rights regarding market entry and exit. The boss-employee and buyout option structures share characteristics of the polyarchy outlined in Sah and Stiglitz (1986) because only the consent of one individual is needed to enact a decision. Of course, real-world decision-making structures may deviate from these ideal types. 上述关于学习的讨论未涉及新企业由创业团队创立时决策是如何制定的。考虑一个由两人组成的创业团队，他们在进入前后从独立来源了解到某个机会的价值。在制定进入/终止和退出/继续决策时，Sah和Stiglitz（1986）提出的理论逻辑暗示了一种概念上简单的映射，适用于创业企业的三种理想决策结构类型。首先，平等伙伴制投票结构具有Sah和Stiglitz（1986）所述的层级制特征：两名企业家都必须同意进入市场，且进入后均需同意留在市场（即不退出）。相反，老板-雇员结构赋予一人决策的绝对权力。介于这两种结构之间的是收购选择权结构。收购选择权结构始于合作关系，但在进入决策时可转换为老板-雇员结构。如果团队成员对机会的价值存在分歧，倾向积极的企业家会通过支付至少等同于对方机会成本的金额收购消极倾向的企业家，实际上是将其聘为雇员，从而获得关于市场进入和退出的全部决策权。老板-雇员结构和收购选择权结构与Sah和Stiglitz（1986）所述的多头政治（polyarchy）特征一致，因为只需一人同意即可执行决策。当然，现实中的决策结构可能偏离这些理想类型。

Confidence Biases in Learning and Decision-Making

学习与决策中的置信偏差

The entrepreneurship literature has identified confidence bias as a key mechanism underlying two well-known empirical regularities associated with erroneous decision-making. The first is that of excess entry, such that too many entrepreneurs enter the market (e.g., Camerer & Lovallo, 1999; Koellinger et al., 2007), and the second is that of delayed exit, such that entrepreneurs persist in the market even when faced with strong evidence that they should terminate operations (Åstebro et al., 2007; DeTienne et al., 2008; Gimeno et al., 1997). More generally, overconfidence in one form or another has come to be viewed as a defining trait of entrepreneurs. In their pioneering survey of 3,000 entrepreneurs, Cooper, Woo, and Dunkelberg (1988) reported that approximately half of entrepreneurs included in their study believed their success likelihood to exceed $9 0 %$ , while, at the same time, they believed that most others had a much lower likelihood of success. Busenitz and Barney (1997: 10) compared a sample of entrepreneurs to a sample of managers and found that their “overconfidence and representativeness variables correctly categorized entrepreneurs and managers more than $7 0 %$ of the time.” Wu and Knott (2006) studied entry into commercial banking and highlighted the distinction between overconfidence in the face of uncertainty about market demand, versus one’s own ability. Other management research focuses on types of confidence biases that may have important implications for entrepreneurial decisions and outcomes (e.g., Camerer & Lovallo, 1999; Dushnitsky, 2010; Hayward, Shepherd, & Griffin, 2006; Lowe & Ziedonis, 2006; Sandri, Schade, Musshoff, & Odening, 2010).4 创业文献已将信心偏差确定为与错误决策相关的两个众所周知的经验规律背后的关键机制。第一个是过度进入，即太多企业家进入市场（例如，Camerer & Lovallo, 1999；Koellinger et al., 2007），第二个是延迟退出，即企业家即使面临应终止经营的有力证据，仍会坚持留在市场中（Åstebro et al., 2007；DeTienne et al., 2008；Gimeno et al., 1997）。更普遍地说，某种形式的过度自信已被视为企业家的一个标志性特征。在他们对3000名企业家的开创性调查中，Cooper、Woo和Dunkelberg（1988）报告称，他们研究中约有一半的企业家认为自己的成功可能性超过90%，同时，他们认为大多数其他人的成功可能性要低得多。Busenitz和Barney（1997：10）将一组企业家与一组管理者进行了比较，发现他们的“过度自信和代表性变量正确分类企业家和管理者的准确率超过70%”。Wu和Knott（2006）研究了进入商业银行业的情况，并强调了面对市场需求不确定性时的过度自信与对自身能力的过度自信之间的区别。其他管理研究关注可能对创业决策和结果产生重要影响的各类信心偏差（例如，Camerer & Lovallo, 1999；Dushnitsky, 2010；Hayward, Shepherd, & Griffin, 2006；Lowe & Ziedonis, 2006；Sandri, Schade, Musshoff, & Odening, 2010）。4

We consider behavioral bias in the context of the entrepreneurial learning processes outlined above. Following Cyert and DeGroot (1974), we conceptualize a learning process as one of Bayesian belief updating. Learning results from feedback signals due to actions taken by firms, be it pre-entry via the development of a prototype, market research, or talking to potential customers, or post-entry from product sales. These signals are inherently noisy, causing uncertainty to diminish rather slowly over time as additional feedback is garnered. While one can employ the adaptively rational Bayesian formulation of Cyert and DeGroot (1974), it is also possible to relax these assumptions and explicitly introduce behavioral bias into the learning process. Bias may be manifest both during the pre-entry period, such that it impacts the entry/termination decision, and post-entry, such that it impacts the exit/continuation decision. 我们在上述概述的创业学习过程中考虑行为偏差。遵循Cyert和DeGroot（1974）的理论，我们将学习过程概念化为贝叶斯信念更新的一种。学习源于企业采取行动后的反馈信号，无论是通过开发原型、市场调研或与潜在客户沟通的进入前阶段，还是产品销售后的进入后阶段。这些信号本质上具有噪声性，随着额外反馈的获取，不确定性会随着时间缓慢减弱。虽然可以采用Cyert和DeGroot（1974）提出的适应性理性贝叶斯公式，但也可以放松这些假设并在学习过程中明确引入行为偏差。偏差可能在进入前阶段显现，从而影响进入/终止决策；也可能在进入后阶段显现，从而影响退出/持续决策。

Recently, psychology researchers have begun to recognize that the overconfidence construct has multiple dimensions and that these dimensions impact learning in different ways. The literature distinguishes between (at least) two forms of overconfidence: “overestimation,” which may manifest as beliefs that the likelihood of success is higher than it actually is, and “overprecision,” which may manifest as too-narrow confidence intervals around a given set of beliefs (Moore & Healy, 2008).5 Empirical research has sometimes confounded these forms of overconfidence. For example, a study with a common research design that seeks to elicit data about overconfidence asks respondents how confident they are that they picked the correct answer, in which case “overestimation and overprecision are one and the same” (Moore & Healy, 2008: 503). We assert that disambiguating these distinct forms of overconfidence is essential to understanding the implications of alternative decision-making structures for performance.6 最近，心理学研究人员开始认识到，过度自信这一概念具有多个维度，且这些维度会以不同方式影响学习。文献中区分了（至少）两种形式的过度自信：“高估”，可能表现为认为成功的可能性高于实际情况的信念；以及“过度精确”，可能表现为围绕一组特定信念的置信区间过窄（Moore & Healy, 2008）。5 实证研究有时会混淆这两种形式的过度自信。例如，一项采用常见研究设计以获取关于过度自信数据的研究，会询问受访者对自己选出正确答案的信心有多大，在这种情况下，“高估和过度精确是一回事”（Moore & Healy, 2008: 503）。我们认为，区分这些不同形式的过度自信对于理解替代决策结构对表现的影响至关重要。6

In the context of learning, overestimation and overprecision are clearly distinct constructs that map onto well-known characteristics of entrepreneurs. Overestimation reflects a positive bias in an entrepreneur’s initial beliefs about the merits of an opportunity (and underestimation reflects a negative bias). Such an entrepreneur would start the learning process believing the opportunity is better than it is in reality. All else being equal, such an entrepreneur is more likely to enter the market and, conditional on entry, is more likely to persist in the market. We designate bias that results from overestimation as “optimism” and its opposite as “pessimism. 在学习的背景下，高估和过度精确是明显不同的概念，它们与企业家众所周知的特征相对应。高估反映了企业家对机会价值的初始信念中的积极偏差（而低估反映了消极偏差）。这样的企业家在开始学习过程时会认为该机会比实际情况更好。在其他条件相同的情况下，这样的企业家更有可能进入市场，并且在进入市场的前提下，更有可能在市场中坚持下去。我们将由高估导致的偏差称为“乐观”，而将其对立面称为“悲观”。

Overprecision is reflected in the confidence interval around an estimated belief that is smaller than necessitated by the uncertainty inherent in the opportunity. This overprecision has important dynamic consequences in a model of learning (Chen et al., 2018; Posen et al., 2018). We follow Moore and Healy (2008) by defining over- and underprecision relative to rational belief updating as determined by Bayes’s rule. In a Bayesian learning model, the optimal rate of belief updating is a function of the noisiness of the feedback signal. When an entrepreneur exhibits overprecision bias, they are too sure that their beliefs are correct and, as a consequence, update their beliefs in the presence of new information less than is warranted by the uncertainty inherent in the signal. In the extreme case, the entrepreneur completely ignores new information. Likewise, underprecision bias is the case in which the entrepreneur responds too strongly (i.e., updates their beliefs too much in response to new information). 过度精确性体现在围绕估计信念的置信区间过小，而这一区间本应大于机会本身所固有的不确定性所要求的范围。这种过度精确性在学习模型中会产生重要的动态后果（Chen et al., 2018；Posen et al., 2018）。我们遵循Moore和Healy（2008）的定义，将相对于理性信念更新（由贝叶斯法则确定）的过度精确性和不足精确性进行区分。在贝叶斯学习模型中，信念更新的最优速率是反馈信号噪声程度的函数。当创业者表现出过度精确性偏差时，他们会过于确信自己的信念是正确的，因此，在面对新信息时，其信念更新的幅度会小于信号所固有的不确定性所应允许的范围。在极端情况下，创业者会完全忽视新信息。同样，不足精确性偏差是指创业者的反应过于强烈（即对新信息的信念更新幅度过大）。

It is not at all obvious how individual biases interact in a team decision-making setting. In principle, there may be conditions under which partners’ biases amplify one another and other situations in which these biases cancel each other out. It may also be the case that alternative decision-making structures are differentially effective at mitigating entrepreneurial bias, such that the most appropriate decision-making structure may be a function of team members’ bias types. 在团队决策场景中，个体偏见如何相互作用，这一点并不明显。原则上，在某些情况下，伙伴的偏见可能会相互放大，而在另一些情况下，这些偏见可能会相互抵消。此外，不同的决策结构在缓解创业偏见方面的效果可能存在差异，因此最合适的决策结构可能取决于团队成员的偏见类型。

Opportunity Costs, Teams, and Entrepreneurial Entry

机会成本、团队与创业进入

Much scholarly literature examines the impact of opportunity costs on entrepreneurial entry (e.g., Shane, 200o). In this literature, an individual enters the market if their expected utility from doing so— that is, the sum of both anticipated pecuniary and nonpecuniary rewards—exceeds the entry costs of setting up the new organization and the opportunity costs of foregone wages in paid employment (Parker, 2009b; Wu & Knott, 2006). Numerous studies build on this framework, implicitly or explicitly, to explain the differential patterns of entrepreneurial entry across the wage spectrum (e.g., Åstebro & Thompson, 2011; Braguinsky, Klepper, & Ohyama, 2012; Elfenbein, Hamilton, & Zenger, 2010; Hamilton, 2000), to examine the role of liquidity constraints on entrepreneurial entry (e.g., Evans & Jovanovic, 1989; Hurst & Lusardi, 2004), and to model the entry decisions of diversifying incumbents (Levinthal & Wu, 2010). 许多学术文献研究机会成本对创业进入的影响（例如，Shane，2000）。在这些文献中，当个体从进入市场中获得的预期效用——即预期的货币和非货币回报之和——超过建立新组织的进入成本以及放弃有薪工作的工资机会成本时（Parker，2009b；Wu & Knott，2006），个体就会进入市场。众多研究基于这一框架，或明或暗地解释不同工资水平下创业进入的差异模式（例如，Åstebro & Thompson，2011；Braguinsky、Klepper & Ohyama，2012；Elfenbein、Hamilton & Zenger，2010；Hamilton，2000），考察流动性约束对创业进入的作用（例如，Evans & Jovanovic，1989；Hurst & Lusardi，2004），并为多元化在位企业的进入决策建模（Levinthal & Wu，2010）。

When the entry decision is preceded by a period of learning, opportunity costs influence which firms enter the market. This has two implications (Chen et al., 2018). First, the extent of the opportunity costs truncates the distribution of entrants’ beliefs about the merits of their opportunities. The higher the costs of entry, the more positively a firm must view its opportunity to cross the market entry threshold. Second, there is a positive correlation between the level of opportunity costs and the time needed for a firm with a poor-quality opportunity to exit. 当进入决策之前存在一段学习期时，机会成本会影响哪些企业进入市场。这有两个含义（Chen等人，2018）。首先，机会成本的高低会截断进入者对自身机会价值信念的分布。进入成本越高，企业必须对其机会有越积极的看法才能跨越市场进入门槛。其次，机会成本水平与拥有低质量机会的企业退出所需时间之间存在正相关关系。

Although previous literature has generated significant scholarly and practical insights, it is premised on depictions of decision-makers as individuals or firms as unitary actors. When teams of individuals are involved in entrepreneurship, their joint access to resources may increase, but the opportunity costs to each individual team member must be considered. Each member of the team must ultimately benefit from entry. To our knowledge, no prior work examines the effect of this requirement on market entry or the tendencies of teams that have similar versus heterogeneous opportunity costs, nor do we know of prior work that examines how different decision-making structures affect entry and exit decisions when opportunity costs among team members are heterogeneous.7 尽管先前的文献产生了大量学术和实践见解，但它以决策者被描绘为个体或企业作为单一行为体为前提。当个体团队参与创业时，他们对资源的共同获取可能会增加，但每个团队成员的机会成本必须被考虑。团队中的每个成员最终都必须从参与中受益。据我们所知，目前尚无研究考察这一要求对市场进入的影响，也没有研究考察具有相似机会成本与异质机会成本的团队的倾向，我们也不清楚是否有先前的研究考察了当团队成员的机会成本异质时，不同的决策结构如何影响进入和退出决策。7

In the next section, we lay out the foundations of our computational model. First, the entrepreneurship process involves learning about an uncertain opportunity: learning pre-entry that informs entry/ termination decisions and learning post-entry that leads to ongoing exit/continuation decisions. Second, at the time of a positive entry decision, entrepreneurs each incur nonrecoverable fixed opportunity costs. Third, entrepreneurs may exhibit Bayesian rationality or confidence biases that cause their beliefs about the merits of their opportunities to deviate from the rational baseline; however, entrepreneurs act rationally conditional on their (potentially biased) beliefs. Finally, entrepreneurial teams make entry and exit decisions based on a decision-making structure that aggregates the beliefs and opportunity costs of all team members. 在下一部分中，我们将阐述我们计算模型的基础。首先，创业过程涉及对不确定机会的学习：进入前的学习会影响进入/终止决策，而进入后的学习会导致持续的退出/继续决策。其次，在做出积极的进入决策时，创业者各自承担不可收回的固定机会成本。第三，创业者可能表现出贝叶斯理性或信心偏差，这会导致他们对自身机会价值的信念偏离理性基准；然而，创业者会根据其（可能存在偏差的）信念采取理性行动。最后，创业团队会根据一种决策结构来做出进入和退出决策，该结构会汇总所有团队成员的信念和机会成本。

COMPUTATIONAL MODEL

计算模型

We developed a simulation model in which multiple agents independently learn about the success prospects of an entrepreneurial opportunity during a pre-entry period. At the end of this period, the agents decide whether to engage in the opportunity by forming a single business and starting operations. The manner by which this decision is made is determined in advance, and our model focuses on three possibilities that are described in more detail below: partnership, boss-employee, and buyout option.8 我们开发了一个模拟模型，在该模型中，多个代理在进入前阶段会独立了解创业机会的成功前景。在该阶段结束时，代理们会决定是否通过成立单一企业并开始运营来参与该机会。决策的方式预先确定，我们的模型重点关注三种可能性，下文将对其进行更详细的描述：合伙制、雇佣制和收购选择权。8

We begin this section by describing the structure of the model, starting with a single-agent model and moving to a multi-agent model. We then exercise our multi-agent model to assess the efficacy of alternative decision-making structures and to highlight the effects of confidence biases across these structures. 我们从描述模型的结构开始介绍本节内容，首先介绍单智能体模型，然后过渡到多智能体模型。接着，我们运用多智能体模型来评估替代决策结构的有效性，并强调这些结构中置信偏差的影响。

Single-Agent Model

单智能体模型

The simulation builds on the single-agent entrepreneurial learning simulation framework of Chen et al. (2018) (henceforth, “CCEP”), which itself adds pre-entry learning and behavioral bias to Ryan and Lippman’s (2003) model of optimal exit from a project with noisy returns. In CCEP, agents costlessly evaluate an opportunity during a pre-entry learning period of length $\Lambda$ (i.e., from $t = - \Lambda$ to 0). During this period, these agents may, for example, engage in market research, build a product prototype, or make contact with potential suppliers. Based on their updated beliefs about success prospects at the end of the pre-entry learning period, agents may opt to pay an entry cost, $k _ { : }$ and enter the market to exploit the potential profits of the opportunity. Entry costs include both the cash costs associated with starting operations and the opportunity costs of foregoing alternative employment. Post-entry, agents accrue actual profits and losses and use these profits and losses to continue to update beliefs about the merits of the opportunity. 该模拟基于Chen等人（2018）的单主体创业学习模拟框架（以下简称“CCEP”）构建，而CCEP本身在Ryan和Lippman（2003）关于具有噪声收益的项目最优退出的模型中加入了进入前学习和行为偏差。在CCEP中，主体在长度为$\Lambda$的进入前学习期（即从$t = -\Lambda$到0）内可免费评估一个机会。在此期间，这些主体可能会进行市场调研、构建产品原型或与潜在供应商建立联系等。在进入前学习期结束时，基于其对成功前景的更新信念，主体可能选择支付进入成本$k_{:}$并进入市场以获取该机会的潜在利润。进入成本包括启动运营的现金成本以及放弃替代就业的机会成本。进入市场后，主体会累积实际利润和损失，并利用这些利润和损失继续更新对该机会价值的信念。

For parsimony, CCEP focuses on two discrete types of opportunities: with probability $p$ , the opportunity is profitable (type $H )$ , with mean profit rate $\mu = \mu _ { \mathrm { H } } > 0$ ; and, with probability $1 - p$ , the opportunity is unprofitable (type $L$ ), with mean profit rate $\mu = \mu _ { \mathrm { L } } < 0$ In either case, profit variance in both the pre- and post-entry periods is $\mathbf { \sigma } ^ { \sigma ^ { 2 } }$ . The signal of cumulative profits, $X _ { t } ,$ that an agent receives follows a Brownian motion with drift $\mu$ and variance $\mathbf { \sigma } ^ { \sigma ^ { 2 } }$ .Following entry, profits are discounted at a rate $\delta > 0$ Though an agent does not know the opportunity type ex ante, they do know the parameters of the underlying Brownian motion. We use $\hat { \boldsymbol p } _ { t }$ to denote an agent’s belief about the probability that the opportunity is type $H$ at time t. As the agent accrues profit signals pre-entry, and actual profits post-entry, $\hat { \boldsymbol p } _ { t }$ is continuously updated to reflect their evolving beliefs. The simulation initiates at $t = - \Lambda$ , which is the start of the pre-entry learning period. A rational agent’s belief that the opportunity is type $H$ at the beginning of the pre-entry period is $\hat { \boldsymbol { p } } _ { - \Lambda } = \boldsymbol { p }$ Assuming the opportunity is type $H , \hat { p } _ { t } \to 1$ as $t \to \infty$ . 为了简洁起见，CCEP 关注两种离散类型的机会：以概率 \( p \)，该机会是有利可图的（类型 \( H \)），平均利润率 \( \mu = \mu_H > 0 \)；以概率 \( 1 - p \)，该机会无利可图（类型 \( L \)），平均利润率 \( \mu = \mu_L < 0 \)。在这两种情况下，进入前和进入后的利润方差均为 \( \sigma^{\sigma^2} \)。代理人收到的累积利润信号 \( X_t \) 遵循漂移为 \( \mu \)、方差为 \( \sigma^{\sigma^2} \) 的布朗运动。进入后，利润按贴现率 \( \delta > 0 \) 贴现。尽管代理人事前不知道机会类型，但他们知道潜在布朗运动的参数。我们用 \( \hat{p}_t \) 表示代理人在时间 \( t \) 时对机会为类型 \( H \) 的概率的信念。随着代理人在进入前累积利润信号、进入后累积实际利润，\( \hat{p}_t \) 会不断更新以反映其不断演变的信念。模拟从 \( t = -\Lambda \) 开始，即进入前学习期的开始。理性代理人在进入前时期开始时对机会为类型 \( H \) 的信念为 \( \hat{p}_{-\Lambda} = p \)。假设机会为类型 \( H \)，当 \( t \to \infty \) 时，\( \hat{p}_t \to 1 \)。

The entry decision is a central element of CCEP. An agent enters if and only if the expected return from the opportunity, as informed by the pre-entry period, exceeds the entry cost, $k$ This expected return, which includes both expected operating profit as well as the option to cut losses by exiting, is a function of $\hat { p } _ { 0 }$ , the agent’s belief about the probability of a type $H$ opportunity at $k = 0$ Thus, an agent’s optimal policy is to enter if $\hat { p } _ { 0 }$ maps to expected returns that exceed $k$ Conditional on entry, the decision to continue is an optimal stopping problem; if the agent’s belief $\hat { \boldsymbol p } _ { t }$ falls below $p ^ { * }$ , itself a function of the key parameters of the model, the agent terminates the business and exits the market.0 Figure 1 depicts the timing of the model. 进入决策是CCEP的核心要素。当且仅当机会的预期回报（由进入前阶段的信息提供）超过进入成本\( k \)时，代理人才会进入。这一预期回报包括预期经营利润以及通过退出止损的选择权，它是\(\hat{p}_0\)的函数，其中\(\hat{p}_0\)是代理在\( k=0 \)时对类型\( H \)机会概率的信念。因此，代理的最优策略是：若\(\hat{p}_0\)对应的预期回报超过\( k \)，则进入。在进入的前提下，继续经营的决策是一个最优停止问题；如果代理的信念\(\hat{p}_t\)低于\( p^* \)（\( p^* \)本身是模型关键参数的函数），则代理终止业务并退出市场。图1描述了模型的时间线。

CCEP incorporates two types of confidencerelated behavioral biases. First, agents may have biased initial beliefs and, as such, may exhibit estimation bias. Values of $\hat { p } _ { - \Lambda } > p$ reflect overestimation (optimism), while $\hat { p } _ { - \Lambda } { < } p$ reflects underestimation (pessimism). Second, agents may have biased beliefs about the noisiness of profit signals and accordingly may exhibit precision bias (Moore & Healy, 2008). Per standard convention, precision $\tau$ is defined as the inverse variance in profit signals (i.e., $\tau = 1 / \sigma ^ { 2 }$ . We use $\hat { \boldsymbol { \tau } }$ to denote the agent’s beliefs on τ. By recognizing that $\hat { \tau } / \tau$ is simply the ratio of the true $\mathbf { \sigma } ^ { \mathrm { ~ \overset { ~ 2 ~ } { ~ } ~ } }$ to the agent’s beliefs on $\mathbf { \sigma } ^ { \sigma ^ { 2 } }$ , $\hat { \tau } / \tau < 1$ reflects overprecision, in that agents update beliefs too slowly (relative to a Bayesian learner) because they believe profit signals to be less informative (i.e., noisier) than they really are. Conversely, $\hat { \tau } / \tau > 1$ reflects underprecision, in that agents update beliefs too rapidly because they believe profit signals to be more informatve (i.., less noisy) than the really r.11 CCEP 包含两种与信心相关的行为偏差。首先，代理人可能有偏差的初始信念，因此可能表现出估计偏差。$\hat{p}{-\Lambda} > p$ 的值反映高估（乐观），而 $\hat{p}{-\Lambda} < p$ 反映低估（悲观）。其次，代理人可能对利润信号的噪声程度有偏差的信念，因此可能表现出精确性偏差（Moore & Healy，2008）。按照标准惯例，精确性 $\tau$ 定义为利润信号的逆方差（即 $\tau = 1/\sigma^2$）。我们用 $\hat{\tau}$ 表示代理人对 $\tau$ 的信念。通过认识到 $\hat{\tau}/\tau$ 只是真实 $\sigma^2$ 与代理人对 $\sigma^2$ 的信念的比值，$\hat{\tau}/\tau < 1$ 反映过高精确性，即代理人更新信念的速度太慢（相对于贝叶斯学习者），因为他们认为利润信号的信息量比实际少（即更嘈杂）。相反，$\hat{\tau}/\tau > 1$ 反映过低精确性，即代理人更新信念的速度太快，因为他们认为利润信号的信息量比实际多（即更不嘈杂）。

$\Lambda$ , which concludes at $t = 0$ when agents make the market-entry decision. If entry occurs, agents evaluate whether to remain in the market continuously following $t = 0$ . $\Lambda$，在$t = 0$时结束，此时参与者做出市场进入决策。如果进入发生，参与者会评估在$t = 0$之后是否持续留在市场中。

Two-Agent Model

双代理模型

We extend the single-agent CCEP framework to two risk-neutral agents.12 We assume that each agent is necessary for operating the enterprise—that is, that each agent has human capital that is essential for investigating and exploiting the opportunity. A firm, then, consists of two agents who form a team prior to entry to investigate a single opportunity. As in CCEP, we assume that, prior to entry, these agents receive signals with independent noise components, drawn from a normal distribution with mean $\mu$ and variance $\mathbf { \sigma } ^ { \sigma ^ { 2 } }$ .Each team member forms unique beliefs about the quality of the opportunity, behaving exactly as they would in CCEP. We assume that the private nature of the pre-entry signals, strategic considerations, and the potential for bias preclude agents from directly and credibly communicating their beliefs to one another; as a result, neither agent makes an inference based upon any information received by their teammate.13 Their decision to commit to joining the firm, however, is credible and contractible. Agents, by definition, commit only if they believe that, by doing so, they will be better off in expectation. 我们将单主体CCEP框架扩展到两个风险中性主体。12 我们假设每个主体对于企业的运营都是必要的——也就是说，每个主体都拥有对机会进行调查和利用至关重要的人力资本。因此，一家企业由两名主体组成，他们在进入前形成一个团队以调查单一机会。与CCEP中一样，我们假设在进入前，这些主体收到带有独立噪声成分的信号，这些信号来自均值为μ、方差为$\mathbf{\sigma}^{\sigma^2}$的正态分布。每个团队成员对机会的质量形成独特的信念，其行为与在CCEP中完全一致。我们假设，进入前信号的私有性、战略考量以及潜在的偏见，使得主体无法直接且可信地相互交流他们的信念；因此，任一主体都不会基于其队友收到的任何信息做出推断。13 然而，他们决定承诺加入企业是可信且可契约化的。根据定义，主体只有在相信这样做会使自己在期望中受益时才会做出承诺。

We further assume that each agent, $j = 1$ , or has their own opportunity cost of entry, $k _ { j } .$ To agree to participate, each agent must expect to receive a reward equal to or greater than their opportunity cost. Following entry, entrants receive either a fixed payment or a share of the profits, depending on their decision-making structure, which we introduce below.14 As in CCEP, we abstract away from liquidity constraints in this model; thus, any agreement that is viewed in expectation as value creating for all parties can be costlessly financed. 我们进一步假定，对于每个主体 \( j = 1 \)，或其自身具有进入的机会成本 \( k_j \)。为同意参与，每个主体必须期望获得的回报等于或大于其机会成本。进入后，参与者根据其决策结构（下文将介绍）获得固定支付或利润分成。与CCEP模型一样，我们在本模型中不考虑流动性约束；因此，任何在预期中被视为对所有方都创造价值的协议都可无成本地融资。 14

With two agents, we must specify a decisionmaking structure that encompasses three related processes to describe firm behavior fully: (a) how the agents in the team decide to enter, (b) how they decide to exit, and (c) how they divide the proceeds of the business conditional on entry. The first two of these correspond to decision rights, and the third corresponds to cash flow rights. We identify three alternative decision-making structures that determine learning aggregation, ownership, and entry/ exit decisions, which we describe below. 有两个代理时，我们必须指定一个决策结构，该结构包含三个相关过程，以全面描述企业行为：(a) 团队中的代理如何决定进入，(b) 他们如何决定退出，以及 (c) 在进入的前提下如何分配企业收益。其中前两个对应决策权，第三个对应现金流权。我们确定了三种决定学习聚合、所有权和进出决策的替代决策结构，如下所述。

Boss-employee (boss). In the boss decisionmaking structure, a pre-identified agent, who we will call agent 1, has both decision rights and cash flow rights as the boss of the firm from the beginning of the pre-entry period. If the boss decides to enter, they must ensure agent 2 earns at least their opportunity costs, $k _ { 2 }$ . This may come in the form of an upfront fixed fee or a periodic payment that, in expectation, is equal to $k _ { 2 }$ , which may be thought of as a wage. The team enters only if agent 1 believes that the expected value of the opportunity exceeds $k _ { 1 } + k _ { 2 }$ . In other words, only agent 1’s beliefs matter for the boss decision-making structure, and her entry threshold is defined by the sum of both agents’ opportunity costs. Conditional on entry, the firm exits if and only if agent 1’s beliefs about the value of the opportunity fall below $p ^ { * }$ The boss’s exit decision is binding and irrevocable for both agents. 15 老板-员工（老板）。在老板决策结构中，从前期开始就预先确定的代理人（我们称之为代理人1）从一开始就作为公司老板拥有决策权和现金流权。如果老板决定进入，他们必须确保代理人2获得至少其机会成本，即\( k_2 \)。这可能以预付固定费用或周期性支付的形式出现，其预期值等于\( k_2 \)，这可以被视为工资。只有当代理人1认为机会的预期价值超过\( k_1 + k_2 \)时，团队才会进入。换句话说，只有代理人1的信念对老板决策结构至关重要，她的进入门槛由两个代理人的机会成本之和定义。在进入的前提下，公司退出的条件是且仅当代理人1对机会价值的信念低于\( p^* \)。老板的退出决策对两个代理人都具有约束力且不可撤销。15

Equal partnership voting (partnership). In the partnership decision-making structure, agents commit at the beginning of the pre-entry learning period to split all post-entry profits equally, and cannot re-contract at any point onward. Entry occurs only if both agents believe that the expected value of a $5 0 %$ share of the profits exceeds their individual opportunity costs. Conditional on entry, each agent receives exactly half of the profits. Since all agents are necessary for the operation of the firm, exit occurs the first time any agent’s beliefs fall below $p ^ { * }$ . At that point, it is optimal for that agent to withdraw their effort.16 平等伙伴投票（合伙制）。在合伙制决策结构中，代理人在进入前学习期开始时承诺将所有进入后的利润平均分配，此后任何时候都不能重新签约。只有当双方代理人都认为获得50%利润份额的预期价值超过其个人机会成本时，才会进入。一旦进入，每个代理人将获得恰好一半的利润。由于所有代理人都是企业运营所必需的，退出发生在任何代理人的信念首次低于\( p^* \)时。此时，该代理人撤回其努力是最优的。16

Buyout option in an equal partnership (buyout). We additionally model a decision-making structure in which agents begin the pre-entry learning period in an equal partnership, but may reallocate decision and cash flow rights at the end of the pre-entry learning period if there is a disagreement. Under buyout, one of three situations follows the learning period: (a) if both agents 1 and 2 believe that the expected value of a $5 0 %$ share of the profits exceeds their opportunity costs— $\mathbf { \mathcal { k } } _ { 1 }$ and $k _ { 2 }$ , respectively—then the firm remains a partnership and enters; (b) if condition (a) is not met, but one agent believes expected profits exceed $k _ { 1 } + k _ { 2 }$ , then the firm enters as a boss structure, where the positively inclined agent pays the negatively inclined agent at least their opportunity costs to work for the firm;17 and (c) if neither agent believes the expected value of total profits exceeds $k _ { 1 } + k _ { 2 }$ , the team does not enter. We note that, post-entry, this decision-making process leads either to a boss structure, where decision-making and profits are consolidated in a single agent, or a partnership structure, where decision-making and profits are divided between two agents. In other words, the buyout option may or may not be exercised. 平等合伙制中的收购选择权（收购）。我们另外构建了一个决策结构：代理人在进入前的学习期开始时处于平等合伙制，但如果存在分歧，他们可能在进入前学习期结束时重新分配决策权和现金流权。在收购情形下，学习期后会出现以下三种情况之一：(a) 如果代理人1和代理人2都认为，各自50%的利润份额的预期价值超过其机会成本——分别为$\mathbf{k}_1$和$\mathbf{k}_2$——那么企业将保持合伙制并进入；(b) 如果条件(a)不满足，但其中一个代理人认为预期利润超过$\mathbf{k}_1 + \mathbf{k}_2$，那么企业将以“老板制”结构进入，其中倾向积极的代理人需向倾向消极的代理人支付至少其机会成本，以使其为企业工作；17 (c) 如果两个代理人都不认为总利润的预期价值超过$\mathbf{k}_1 + \mathbf{k}_2$，则团队不进入。我们注意到，进入后，这一决策过程要么导致“老板制”结构（决策权和利润集中在单个代理人手中），要么导致合伙制结构（决策权和利润在两个代理人之间分配）。换句话说，收购选择权可能被行使，也可能不被行使。

We note that, when it comes to entry, the partnership structure relates closely to the “hierarchy” decision-making structure described by Sah and Stiglitz (1986), insofar as all agents must agree for entry to proceed. By contrast, the buyout structure relates to Sah and Stiglitz’s (1986) “polyarchy” decisionmaking structure, insofar as only a single agent must take ownership for entry to proceed. 我们注意到，在涉及进入（阶段）时，这种合作结构与Sah和Stiglitz（1986）所描述的“层级制”决策结构密切相关，因为所有参与者必须达成一致才能推进进入流程。相比之下，收购结构则与Sah和Stiglitz（1986）的“多元制”决策结构相关，因为只需单个参与者承担所有权即可推进进入流程。

Simulation Output

模拟输出

The computational simulation produces a rich data stream at both the individual agent and firm levels, which enables us to compare the performance of different team structures and tie these performance differences to specific mechanisms. At each point in time, our model records what each agent believes about the probability that their opportunity is type $H .$ For teams that decide to enter, the model additionally records profits and losses during each period of operation, total profit net of opportunity costs, and the time of exit for those firms that choose to shut down. 计算模拟在个体代理和企业层面产生了丰富的数据流，这使我们能够比较不同团队结构的表现，并将这些表现差异与特定机制联系起来。在每个时间点，我们的模型记录每个代理对其机会为H型的概率的信念。对于决定进入的团队，模型还记录每个运营期间的利润和损失、扣除机会成本后的总利润，以及选择关闭的企业的退出时间。

We focus primarily on the expected value of new venture profits conditional on the team’s decisionmaking structure and agents’ opportunity costs. In all simulations, we fix $p = . 5 0$ , $\mu _ { \mathrm { H } } = + 5 0$ , $\mu _ { \mathrm { L } } = - 5 0$ and $\ S = 0 . 1$ . Unless otherwise specified, we set $k _ { 1 } =$ $k _ { 2 } = 5 0$ , and simulate one million two-agent teams. We vary the length of the pre-entry learning period $\left( \Lambda \right)$ , as well as agents’ initial beliefs $( \hat { p } _ { - \Lambda } )$ and their beliefs about the precision of the signals they receive $( \hat { \boldsymbol { \tau } } / \tau )$ . 我们主要关注新企业利润的期望值，该期望值取决于团队的决策结构和代理人的机会成本。在所有模拟中，我们固定 \( p = 0.5 \)，\( \mu_{\mathrm{H}} = +50 \)，\( \mu_{\mathrm{L}} = -50 \) 和 \( S = 0.1 \)。除非另有说明，我们将 \( k_1 = k_2 = 50 \)，并模拟一百万支两代理人团队。我们改变进入前学习期的长度 \( (\Lambda) \)，以及代理人的初始信念 \( (\hat{p}_{-\Lambda}) \) 和他们对所接收信号精度的信念 \( (\hat{\tau}/\tau) \)。

Given that $p , \mu _ { \mathrm { H } } , \mu _ { \mathrm { L } }$ , and δ are fixed, performance is determined by the cost and incidence of three types of errors: (a) mistaken entry, in which type $L$ teams mistakenly enter; (b) mistaken nonentry, in which type $H$ teams mistakenly fail to enter at all; and (c) mistaken exit, in which type $H$ teams enter but subsequently leave the market mistakenly. The left-hand panel of Figure 2 shows how type $L$ and type $H$ firms sort into groups defined by these errors. Since type L teams that enter suffer both the opportunity costs of entry and accumulated losses as long as they stay in the market, the cost of mistaken entry is a function of both $k _ { 1 } + k _ { 2 }$ and how long it takes type L entrants to exit the market. The cost of mistaken nonentry represents the foregone stream of earnings from an opportunity that would have succeeded, and is thus characterized by the unrealized perpetuity value of a type $H$ team $\mathrm { ( \mu _ { H } / \delta ) }$ less the entry cost of the agents $\left( k _ { 1 } \ + \ k _ { 2 } \right)$ . The cost of mistaken exit can be characterized the same way as mistaken nonentry, treating the entry costs as sunk and starting from the time the type $H$ team erroneously exits. Given that \( p \), \( \mu_{\mathrm{H}} \), \( \mu_{\mathrm{L}} \), and \( \delta \) are fixed, performance is determined by the cost and incidence of three types of errors: (a) mistaken entry, in which type \( L \) teams mistakenly enter; (b) mistaken nonentry, in which type \( H \) teams mistakenly fail to enter at all; and (c) mistaken exit, in which type \( H \) teams enter but subsequently leave the market mistakenly. The left-hand panel of Figure 2 shows how type \( L \) and type \( H \) firms sort into groups defined by these errors. Since type L teams that enter suffer both the opportunity costs of entry and accumulated losses as long as they stay in the market, the cost of mistaken entry is a function of both \( k_1 + k_2 \) and how long it takes type L entrants to exit the market. The cost of mistaken nonentry represents the foregone stream of earnings from an opportunity that would have succeeded, and is thus characterized by the unrealized perpetuity value of a type \( H \) team \( (\mu_{\mathrm{H}} / \delta) \) less the entry cost of the agents \( (k_1 + k_2) \). The cost of mistaken exit can be characterized the same way as mistaken nonentry, treating the entry costs as sunk and starting from the time the type \( H \) team erroneously exits.

FIGURE 2 Comparison of Decision Errors for Two-Agent Teams of Unbiased Agents
图2 无偏智能体双智能体团队的决策误差比较

0 l $\mathbf { x }$ axis on each graph is the number of periods post-entry. The top half of each graph represents the decisions of 5,000 type $L$ teams, and the bottom half represents the decisions of 5,000 type $H$ tThe be o Nn type $L$ teams that did not enter. “Entry mistakes” indicates the proportion of type $L$ teams in the market, and “Exited” represents the proportion of type $L$ teams that have exited the market. “In market” represents type $H$ teams in the market. “Exit mistakes” represents type $H$ teams that entered the market but subsequently exited. “Nonentry mistakes” represents the proportion of type $H$ teams that fail to enter altogether. For structure of interest. 0轴上每个图表的横轴是进入后的周期数。每个图表的上半部分代表5000个L型团队的决策，下半部分代表5000个H型团队的决策。“未进入的L型团队”表示未进入市场的L型团队比例。“进入错误”表示市场中L型团队的比例，“退出”表示已退出市场的L型团队比例。“在市场中”表示市场中的H型团队。“退出错误”表示进入市场但随后退出的H型团队。“未进入错误”表示完全未能进入的H型团队比例。为了研究结构。

Figure 2 shows the relative incidence of each type of error by decision-making structure for two unbiased agents with equal opportunity costs $k _ { 1 } = k _ { 2 } =$ 50 and $\Lambda = 1$ .Partnership generates the fewest entry mistakes but the most nonentry mistakes, consistent with the conservatism borne by requiring both agents to agree to the entry decision. Boss has intermediate levels of both entry mistakes and nonentry mistakes. Buyout has the most entry mistakes but the fewest nonentry mistakes, which follows from requiring only one agent to have beliefs above the entry threshold for entry to occur. Furthermore, when the buyout option is exercised, exit will be determined by the firm’s single owner, who, by virtue of deciding to buy out their negatively inclined partner, is likely to be optimistic. Therefore, the single-owner boss who exercises a buyout option suffers a winner’s curse, which exacerbates entry mistakes. These contrasting levels of each type of error point to the key mechanisms underlying the main findings in our experiments. We now provide detailed analyses of these experiments. 图2展示了在决策结构下，两种机会成本相等（\(k_1 = k_2 = 50\)）且\(\Lambda = 1\)的无偏代理者中，每种错误类型的相对发生率。合作制产生的进入错误最少，但非进入错误最多，这与要求两名代理者都同意进入决策所带来的保守倾向一致。老板制在进入错误和非进入错误方面均处于中间水平。买断制的进入错误最多，但非进入错误最少，这是因为仅需一名代理者的信念高于进入阈值即可发生进入。此外，当买断选项被行使时，退出将由公司的单一所有者决定，由于决定买断其倾向负面的合作伙伴，该所有者很可能较为乐观。因此，行使买断选项的单一所有者老板会遭受赢家诅咒，这加剧了进入错误。每种错误类型的这些对比水平揭示了我们实验中主要发现背后的关键机制。我们现在对这些实验进行详细分析。

RESULTS

结果

We begin by examining the performance of the three different decision-making structures—boss, partnership, and buyout—on populations of agents who differ in the nature of their biases. We first use the model to describe the relative performance with identical unbiased, Bayesian agents. We show that, with these agents, partnership is the optimal structure, so long as team members’ opportunity costs of entry are not too different from one another. With unbiased Bayesian agents, we additionally investigate how the relative advantage of partnership over the other structures varies with the amount of pre-entry learning. Next, we fix entry costs and examine the relative performance of the three decision-making structures with a population of agents that is, on average, unbiased, but contains agents with a distribution of estimation and precision biases. With a population of on-average-unbiased agents, buyout becomes the optimal structure. Third, we relax the assumption that the population has a zero mean bias and identify the boundary conditions in terms of population-level estimation and precision biases that define when buyout dominates partnership and vice versa. 我们首先考察三种不同决策结构——老板制、合伙制和买断制——在具有不同偏见性质的代理人群体中的表现。我们首先使用模型描述具有相同无偏贝叶斯代理的相对表现。我们表明，在这些代理中，只要团队成员的进入机会成本彼此不太不同，合伙制就是最优结构。对于无偏贝叶斯代理，我们还研究了合伙制相对于其他结构的相对优势如何随进入前学习量的变化而变化。接下来，我们固定进入成本，考察由平均无偏但包含具有估计和精度偏差分布的代理组成的代理人群体中三种决策结构的相对表现。在平均无偏的代理人群体中，买断制成为最优结构。第三，我们放宽群体零均值偏差的假设，并根据群体层面的估计和精度偏差确定买断制主导合伙制以及反之亦然的边界条件。

We augment this analysis with two sets of extensions that highlight the utility of our computational model. First, we compare the relative post-entry performance and bias characteristics of firms that enter as a single-owner decision-making structure versus a partnership. Here, we examine how selection influences the population of entrants upon which empirical analyses would typically be based and use our model to generate novel predictions for empirical study. Second, we hold the biases of the potential entrepreneurs fixed, and determine the optimal structure for each combination of biases (i.e., agent 1’s initial estimation bias and precision bias; agent 2’s initial estimation bias and precision bias). This further demonstrates the utility of our framework in generating managerially relevant recommendations to teams of prospective entrepreneurs. 我们通过两组扩展分析来增强这一研究，以凸显我们计算模型的有效性。首先，我们比较了以单一所有者决策结构和合伙企业形式进入的企业的相对进入后绩效和偏差特征。在此，我们考察选择如何影响经验分析通常所依据的进入者群体，并利用我们的模型为实证研究生成新颖的预测。其次，我们将潜在创业者的偏差固定，为每种偏差组合（即代理人1的初始估计偏差和精度偏差；代理人2的初始估计偏差和精度偏差）确定最优结构。这进一步证明了我们的框架在为潜在创业者团队生成具有管理相关建议方面的实用性。

Comparison of Decision-Making Structures with Identical Bayesian-Rational Agents

具有相同贝叶斯理性代理的决策结构比较

Our first computational experiment employs only Bayesian-rational agents—agents who have the correct initial beliefs (i.e., rational with $\hat { p } _ { - \Lambda } = 0 . 5$ and who update their beliefs accurately (i.e., Bayesian with $\hat { \tau } / \tau = 1$ —and identical opportunity costs $k _ { 1 } =$ $k _ { 2 } = 5 0$ We vary the length of the pre-entry learning period $\Lambda$ from 0.1 to 5. We interpret $\Lambda = 0 . 1$ as indicating that the pre-entry learning period is very short, leading the pre-entry information collected to be relatively noisy, and $\Lambda = 5$ as indicating that the pre-entry learning period is very long, meaning that the pre-entry information collected is relatively precise. Our focus throughout is on how total expected profits of the team respond to the decision-making structure in question. We abstract away from bargaining power considerations, which might lead to the selection of one structure over the other or alter the profit split between agents. Figure 3 shows the relative performance for boss, partnership, and buyout at each level of A. As $\Lambda$ increases, prospective entrepreneurs make fewer entry and exit mistakes, and the average value created by entrepreneurial teams increases. For Bayesian-rational agents with equal opportunity costs, teams organized as partnerships generate the greatest value, regardless of the length of the pre-entry learning period. Partnership’s relative advantage over boss is $1 %$ with low pre-entry information $\Lambda = 0 . 1$ , rises to nearly $5 %$ at moderate information levels, and declines back to about $1 %$ at high levels $\Lambda = 5$ . Relative to boss, the reduction of mistaken entry produced by partnership more than compensates for the increase in mistaken nonentry, although entry behavior converges as $\Lambda$ approaches infinity. 我们的首个计算实验仅采用贝叶斯理性主体——即具有正确初始信念（即理性，其中 $\hat{p}_{-\Lambda}=0.5$）且能准确更新信念（即贝叶斯更新，其中 $\hat{\tau}/\tau=1$）的主体——以及相同的机会成本 $k_1=k_2=50$。我们将进入前学习期长度 $\Lambda$ 从 0.1 变化到 5。我们将 $\Lambda=0.1$ 解释为进入前学习期非常短，导致收集的进入前信息相对嘈杂；而 $\Lambda=5$ 则表示进入前学习期非常长，意味着收集的进入前信息相对精确。我们始终关注团队总预期利润如何响应所讨论的决策结构。我们暂不考虑议价能力因素，这些因素可能导致选择一种结构而非另一种，或改变主体间的利润分配。图 3 展示了在每个 $\Lambda$ 水平下，老板制、合伙制和买断制的相对表现。随着 $\Lambda$ 增加，潜在创业者的进入和退出错误减少，创业团队创造的平均价值增加。对于机会成本相等的贝叶斯理性主体，无论进入前学习期长度如何，采用合伙制组织的团队创造的价值最大。合伙制相对于老板制的优势在低进入前信息 $\Lambda=0.1$ 时为 1%，在中等信息水平时上升至近 5%，在高信息水平 $\Lambda=5$ 时又回落至约 1%。与老板制相比，合伙制减少的错误进入足以弥补错误不进入的增加，尽管随着 $\Lambda$ 趋近于无穷大，进入行为会收敛。

Somewhat paradoxically, adding the buyout option destroys value when all agents are Bayesianrational. For these agents, entry mistakes resulting from the winner’s curse (i.e., the “curse” from the likelihood that at least one agent will overestimate the probability of success) are particularly costly. With small amounts of pre-entry information, the winner’s curse is modest: buyout performs $4 %$ worse than boss when $\Lambda = 0 . 1$ . With moderate amounts of pre-entry information, however, the winner’s curse is at its most severe: buyout performs $1 0 %$ worse than boss from about $\Lambda = 0 . 3$ to 1. For Bayesianrational agents, then, the flexibility afforded by buyout comes with a cost that varies in severity as a function of pre-entry information. Somewhat paradoxically, adding the buyout option destroys value when all agents are Bayesian rational. For these agents, entry mistakes resulting from the winner’s curse (i.e., the “curse” from the likelihood that at least one agent will overestimate the probability of success) are particularly costly. With small amounts of pre-entry information, the winner’s curse is modest: buyout performs 4% worse than boss when Λ = 0.1. With moderate amounts of pre-entry information, however, the winner’s curse is at its most severe: buyout performs 10% worse than boss from about Λ = 0.3 to 1. For Bayesian rational agents, then, the flexibility afforded by buyout comes with a cost that varies in severity as a function of pre-entry information.

We next examine the relative performance of boss, partnership, and buyout when opportunity costs vary. Our main concern here is with the distribution rather than the total level of opportunity costs. To examine this, we hold constant $k _ { 1 } + k _ { 2 } = 1 0 0$ and vary $k _ { 1 }$ from 0 to 50. Figure 4 depicts the results of asymmetric opportunity costs for differing lengths of pre-entry learning. 接下来，我们考察当机会成本变化时，老板制、合伙制和收购制的相对表现。我们在这里主要关注的是机会成本的分布，而非其总量水平。为了研究这一点，我们固定 \( k_1 + k_2 = 100 \)，并将 \( k_1 \) 从 0 变化到 50。图 4 描绘了不同前期学习时长下非对称机会成本的结果。

As Figure 4 indicates, the supremacy of partnership breaks down when the agents’ opportunity costs differ significantly; that is, when $k _ { 2 } > k _ { 1 }$ .For modest amounts of pre-entry learning—that is, $\Lambda <$ 2—partnership provides the best organizational form only when the two agents’ opportunity costs are relatively similar. As the two agents’ opportunity costs become more asymmetric, partnership’s performance worsens, boss generates the highest expected profits, and buyout also overtakes partnership. The mechanism for this result is intuitive: when a team includes a high-opportunity cost agent and pre-entry learning is limited, mistaken nonentry by type $H$ teams is exacerbated by the partnership structure. This is because, with a short $\Lambda$ , the high-opportunity cost agent is less likely to be sure that their payoff from entry will be positive, and therefore more likely to veto entry even when the opportunity is type $H .$ By contrast, single-agent ownership structures allow the boss to pay the employee their opportunity costs directly if the boss believes expected profits are large enough to cover $k _ { 1 } + k _ { 2 }$ . In other words, when opportunity costs are asymmetric, boss and buyout decision-making structures are relatively insulated against the heightened nonentry mistakes that plague a partnership. Finally, Figure 4 shows that, for unbiased agents, longer pre-entry learning periods erase the problems of partnership when opportunity costs are heterogeneous. When pre-entry knowledge is sufficiently comprehensive, teams make correct decisions irrespective of opportunity cost asymmetry. Pre-entry learning also mitigates the buyout’s winner’s curse; at $\Lambda = 5$ , structure has limited impact on performance with rational agents, regardless of opportunity cost distribution. 如图4所示，当代理人的机会成本存在显著差异时（即\( k_2 > k_1 \)），合作制的优势会瓦解；也就是说，当\( k_2 > k_1 \)时，合作制的优势会消失。对于适度的进入前学习量（即\( \Lambda < 2 \)），只有当两个代理人的机会成本相对相似时，合作制才是最优的组织形式。随着两个代理人的机会成本变得更加不对称，合作制的表现会恶化，老板制产生最高的预期利润，而收购制也会超过合作制。这一结果的机制很直观：当一个团队包含高机会成本的代理人且进入前学习有限时，H型团队的错误非进入行为会因合作制结构而加剧。这是因为，当\( \Lambda \)较小时，高机会成本的代理人不太确定其进入后的收益是否为正，因此即使是H型机会，也更有可能否决进入。相比之下，单代理人所有权结构允许老板在认为预期利润足够覆盖\( k_1 + k_2 \)时，直接向员工支付其机会成本。换句话说，当机会成本不对称时，老板制和收购制的决策结构相对能免受合作制所困扰的加剧的非进入错误的影响。最后，图4显示，对于无偏代理人，当机会成本异质时，较长的进入前学习期会消除合作制的问题。当进入前知识足够全面时，团队会根据机会成本的不对称性做出正确决策。进入前学习还能减轻收购制的赢家诅咒；在\( \Lambda = 5 \)时，无论机会成本分布如何，理性代理人的结构对绩效的影响有限。

FIGURE 3 Partnership Is Superior to Buyout and Boss with Deterministically Unbiased Agents
图3 合作优于收购且管理者具有确定性无偏代理

a function of pre-entry learning duration $\Lambda$ The bottom panel plots the average performances of deterministically unbiased agents each under the boss and buyout decision-making structures relative to partnership performance (top panel) $( % )$ , as function of $\Lambda$ . For example, given $\Lambda = 2$ , performance under buyout is on average ${ \sim } 7 . 5 %$ worse than performance under partnership. A log-scale is applied to the $\mathbf { x }$ axis. 作为预先学习时长 $\Lambda$ 的函数，底部面板展示了在老板（boss）和买断（buyout）决策结构下，确定性无偏代理（agents）各自的平均表现相对于合作关系表现（顶部面板）的百分比（%），其中 $\Lambda$ 为自变量。例如，当 $\Lambda = 2$ 时，买断决策下的表现平均比合作关系下差约 7.5%。x 轴采用对数刻度。

As the discussion above indicates, our model highlights two prospective solutions to remedy partnership’s problem in handling asymmetric opportunity costs: (a) changing the decision-making structure or (b) maintaining the partnership structure but extending pre-entry learning. A third solution also exists: (c) changing the equity distribution to mimic the ratio of opportunity costs.18 In other words, set the equity share of agent 1 to $k _ { 1 } / ( k _ { 1 } + k _ { 2 } )$ and the equity share of agent 2 to $k _ { 2 } /$ $\left( k _ { 1 } + k _ { 2 } \right)$ . Figure A1 in the Appendix shows how this remedy restores partnership’s supremacy with unbiased agents. While, theoretically, this is a rather obvious solution, we note that empirical evidence suggests that relatively few entrepreneurial teams adopt this approach. For instance, the vast majority $( 8 9 % )$ of two-owner ventures in the Kauffman Firm Survey (KFS) report an approximate 50:50 (within $5 %$ ) split in returns, suggesting that partnerships tend to default to a 50:50 division of equity irespective of individuals’ opportunity costs (Ewing Marion Kauffman Foundation, 2013).19 如前所述，我们的模型提出了两种解决伙伴关系在处理非对称机会成本问题的潜在方案：(a) 改变决策结构，或 (b) 维持伙伴关系结构但延长进入前学习期。第三种方案也存在：(c) 调整股权分配以模仿机会成本的比例。18 换句话说，将代理人 1 的股权份额设为 \( k_1 / (k_1 + k_2) \)，将代理人 2 的股权份额设为 \( k_2 / (k_1 + k_2) \)。附录中的图 A1 展示了这一补救措施如何在无偏代理人的情况下恢复伙伴关系的优势地位。虽然从理论上讲，这是一个相当明显的解决方案，但我们注意到经验证据表明，相对较少的创业团队采用这种方法。例如，考夫曼企业调查（KFS）中绝大多数（89%）的双业主企业报告称，回报分配大致为 50:50（误差在 5% 以内），这表明伙伴关系往往默认采用 50:50 的股权分配，而不考虑个人的机会成本（Ewing Marion Kauffman Foundation, 2013）。19

FIGURE 4 Partnership Performance Declines with Unequal Opportunity Costs
图4 合作绩效随机会成本不均而下降

100. The $\mathbf { x }$ -axis represents the proportion of total entry costs possessed by agent 1. For example, at ${ \bf x } = { \bf 0 . 3 }$ , agent 1’s opportunity costs are $k _ { 1 } =$ 30, and agent 2’s opportunity costs are $k _ { 2 } = 7 0$ The graphs are each symmetric around ${ \bf x } = { \bf 0 . 5 }$ .
101. The $\mathbf{x}$-axis represents the proportion of total entry costs possessed by agent 1. For example, at $\mathbf{x} = \mathbf{0.3}$, agent 1’s opportunity costs are $k_1 = 30$, and agent 2’s opportunity costs are $k_2 = 70$. The graphs are each symmetric around $\mathbf{x} = \mathbf{0.5}$.

Comparison of Decision-Making Structures with a Population of Mean-Unbiased Agents

具有无偏均值代理群体的决策结构比较

In the prior section, we assumed that potential entrepreneurs were known not to have decisionmaking biases. In this section, we relax this assumption and assume that potential entrepreneurs’ decision-making biases are unknown, but are drawn from “neutral” distributions with zero mean bias. In other words, we consider a population of potential entrepreneurs that is unbiased on average, but whose agents individually exhibit a range of estimation and precision biases. Specifically, for each agent i, we draw initial beliefs about the likelihood of being type $H _ { \mathrm { { ; } } }$ $\hat { p } _ { - \Lambda }$ , from a $\beta ( 2 , 2 )$ distribution, which partially mimics the attributes of a normal distribution but over the range 0 to 1. We independently draw each agent’s precision bias, $\hat { \tau } / \tau = 2 ^ { X }$ , where $X \sim 4$ . $\beta ( 2 , 2 ) - 2$ , setting the range of precision from 0.25 to 4.20 We plot these distributions in Figure A2 in the Appendix. In choosing these distributions, we seek to represent (a) a population of nascent entrepreneurs that has neutral bias, on average and at the median, but does have variance in both initial estimation and precision biases; and (b) a process whereby individual entrepreneurs do not consciously match according to similarities or differences in estimation or precision bias when forming teams.21 As our interest is in understanding the relative performance of partnership, boss, and buyout in this and in subsequent sections, we equalize each agent’s opportunity costs and hold them constant $( k _ { 1 } = k _ { 2 } = 5 0 )$ . We again vary the length of the preentry learning period $\Lambda$ from 0.1 to 5. 在上一节中，我们假设潜在创业者没有决策偏差。在本节中，我们放松这一假设，假设潜在创业者的决策偏差未知，但来自均值为零偏差的“中性”分布。换句话说，我们考虑一个平均无偏的潜在创业者群体，但其中的个体表现出一系列估计偏差和精度偏差。具体而言，对于每个个体 i，我们从 β(2, 2) 分布中抽取关于自身类型 H 的可能性的初始信念 $\hat{p}_{-\Lambda}$，该分布部分模仿正态分布的属性，但范围在 0 到 1 之间。我们独立抽取每个个体的精度偏差 $\hat{\tau}/\tau = 2^X$，其中 $X \sim \beta(2, 2) - 2$，将精度范围设置为 0.25 到 4.20。我们在附录中的图 A2 中绘制了这些分布。在选择这些分布时，我们试图表示：(a) 一个平均和中位数无偏的新生创业者群体，但在初始估计和精度偏差方面存在差异；以及 (b) 个体创业者在组建团队时不会根据估计或精度偏差的相似性或差异性有意识地进行匹配。21 由于我们的兴趣在于理解本部分及后续部分中合伙企业、老板制和收购制的相对表现，我们将每个个体的机会成本相等并保持不变（$k_1 = k_2 = 50$）。我们再次将进入前学习期的长度 $\Lambda$ 从 0.1 变化到 5。

We plot the relative performance of the three decision-making structures in Figure 5. With onaverage-unbiased agents drawn from the distributions detailed above, partnership is no longer the structure that generates the best results. In this case, buyout and boss are both superior or equal to partnership across the full range of pre-entry durations that we examine. The disparity is greatest at $\Lambda = 0 . 1$ when buyout and boss outperform partnership by $5 5 . 5 %$ and $1 4 . 6 %$ , respectively. The performance difference among all three decision-making structures becomes small beyond $\Lambda = 2$ .22 我们在图5中绘制了三种决策结构的相对性能。在从上述详细分布中抽取的平均无偏代理的情况下，合作不再是产生最佳结果的结构。在这种情况下，在我们研究的整个进入前持续时间范围内，收购和老板结构均优于或等同于合作结构。当收购和老板结构分别比合作结构高出55.5%和14.6%时，差异在Λ=0.1时最大。当Λ超过2.22时，三种决策结构之间的性能差异变得很小。

These results indicate that buyout is clearly more robust in handling agents with a range of (uncorrelated) biases than the other decision-making structures we examine. Why is this the case? Intuitively, the reason is that biases introduce two particularly problematic types of teams that are nonexistent with deterministically unbiased agents: pessimistic partnerships, wherein entrepreneurial teams including at least one pessimist are organized as partnerships; and optimistic buyouts, wherein teams including at least one optimist are organized as buyouts. Pessimists in a partnership exacerbate that structure’s tendency to make nonentry mistakes, while optimists in a buyout exacerbate its tendency to make entry mistakes. While pessimistic partnerships and optimistic buyouts are equally prevalent, by assumption, in a mean-unbiased population, they are not equal in terms of impact on profits. Pessimistic partnerships are worse, because they induce mistaken nonentry that leads to irreversible foregone gains, in contrast to optimistic buyouts whose entry mistakes can be mitigated by exit. Thus, buyout is the superior decision-making structure when the population has a distribution of biases that is meanunbiased. 这些结果表明，在处理具有不同（不相关）偏差的代理时，收购显然比我们研究的其他决策结构更稳健。为什么会这样？直观地说，原因在于偏差会引入两种特别棘手的团队类型，而确定性无偏代理不存在这两种类型：悲观型合伙制，即至少包含一名悲观主义者的创业团队以合伙制形式组织；以及乐观型收购制，即至少包含一名乐观主义者的团队以收购制形式组织。合伙制中的悲观主义者会加剧该结构做出非进入错误的倾向，而收购制中的乐观主义者会加剧其做出进入错误的倾向。虽然根据假设，在均值无偏的群体中，悲观型合伙制和乐观型收购制同样普遍，但它们对利润的影响并不相同。悲观型合伙制更糟糕，因为它们会导致错误的非进入决策，从而带来不可逆转的错失收益，而乐观型收购制的进入错误可以通过退出来缓解。因此，当群体的偏差分布是均值无偏时，收购制是更优的决策结构。

FIGURE 5 Buyout Is Superior to Partnership and Boss in an On-Average-Unbiased Population of Biased Agents
图5 买断制在存在偏差代理的平均无偏总体中优于合伙制和老板制

Noes We reer t agents with estimaion bia drawn from a β(2,) distribution and precision bas drawn om a $\log _ { 2 } \beta ( 2 , 2 )$ distribution the partnership decision-making structure as a function of pre-entry learning duration, $\Lambda$ The bottom panel plots the average performances of 1 performance (top panel) $( % )$ , as a function of $\Lambda$ For example, given $\Lambda = 0 . 5$ , performance under buyout is, on average, ${ \sim } 1 5 %$ better than performance under partnership. A log-scale is applied to the $\mathbf { x }$ axis. Noes We reer t agents with estimaion bia drawn from a β(2,) distribution and precision bas drawn om a $\log _ { 2 } \beta ( 2 , 2 )$ distribution the partnership decision-making structure as a function of pre-entry learning duration, $\Lambda$ The bottom panel plots the average performances of 1 performance (top panel) $( % )$ , as a function of $\Lambda$ For example, given $\Lambda = 0 . 5$ , performance under buyout is, on average, ${ \sim } 1 5 %$ better than performance under partnership. A log-scale is applied to the $\mathbf { x }$ axis.

Figure 6 supports this intuition that the buyout advantage arises from the costs generated by pessimistic agents in partnerships relative to the costs of optimistic agents in buyouts. Panel A contrasts the profit contribution of type $L$ and type $H$ firms organized via buyout and partnership, respectively, as a function of agent 1’s initial beliefs. (Note that the biases of agents 1 and 2 are independent, so a symmetric figure exists for agent 2 as well). Profit contribution reflects the mean profit of a population of entrepreneurial teams according to teams with a given profile (e.g., type $H$ and buyout) and a given agent 1 bias (see Note following Figure 6 for a detailed explanation). Profit contribution values may be positive or negative. Panel B plots the differences in these contributions. Per Panel B, when the team includes a pessimist with $\hat { p } _ { - \Lambda } = 0 . 3$ , there is a buyout advantage of 3.62. By contrast, when the team includes an optimist with $\hat { p } _ { - \Lambda } = 0 . 7$ , partnership generates an advantage of 2.57. Since our distribution contains an identical number of optimistic and pessimistic agents, by construction, the net effect is an overall buyout advantage of 1.05 when comparing this matched pair $\left( + 0 . 2 , - 0 . 2 \right)$ of biased initial beliefs. The total advantage is significantly larger because we integrate over the entire range of pessimist/optimist pairs. 图6支持这一直觉，即收购优势源于合伙企业中悲观代理人产生的成本相对于收购中乐观代理人产生的成本。面板A对比了分别通过收购和合伙组织的L型和H型企业的利润贡献，这一贡献是代理人1初始信念的函数（请注意，代理人1和2的偏差是独立的，因此代理人2也存在对称图形）。利润贡献反映了创业团队总体的平均利润，根据具有特定特征（例如H型和收购）的团队以及特定的代理人1偏差（有关详细说明，请参见图6后的注释）。利润贡献值可以为正或负。面板B绘制了这些贡献的差异。根据面板B，当团队包含悲观主义者（$\hat{p}{-\Lambda}=0.3$）时，收购优势为3.62。相比之下，当团队包含乐观主义者（$\hat{p}{-\Lambda}=0.7$）时，合伙制产生了2.57的优势。由于我们的分布中乐观和悲观代理人的数量相同，因此通过构造，当比较这对偏差初始信念（+0.2，-0.2）时，净效应是总体收购优势为1.05。总优势明显更大，因为我们整合了悲观主义者/乐观主义者对的整个范围。

FIGURE 6 Why Buyout Is Superior to Partnership in an On-Average-Unbiased Population of Biased Agents
图6 在存在偏差代理的平均无偏总体中，收购为何优于合伙制

Notes: In both panels, $\Lambda = 1$ $\log _ { 2 } \beta ( 2 , 2 )$ distribution. The $\mathbf { x }$ o F example, the left panel indicates that type $L$ byout teams for which agent 1’s initial optimism is 0.3 contribute 18 to the mean profit of the population. Thus, to obtain the overall mean profit for type $L$ buyouts, we would sum over the plotted values for the type $L$ buyout line in 0.1 increoptimistic buyouts. Notes: In both panels, $\Lambda = 1$ $\log _ { 2 } \beta ( 2 , 2 )$ 分布。左面板中，例如，类型 $L$ 的收购团队中，代理 1 的初始乐观度为 0.3 的团队对群体平均利润的贡献为 18。因此，为了获得类型 $L$ 收购的总体平均利润，我们需要对类型 $L$ 收购线中以 0.1 为增量的乐观收购（值）进行求和。

The results of this section, contrasted with those of the previous section, highlight the effects of introducing bias into decision-making agreements. When agents have a range of biases, buyout generates the best performance, due to the greater cost of irreversible mistaken nonentry relative to mistaken entry that can be corrected through exit. This makes pessimistic teams more damaging when organized via partnerships than are optimistic teams when organized via buyouts; as a result, buyout is the more robust decision-making structure when agents are symmetrically distributed around neutral biases. Moreover, partnership generates especially poor performance when pre-entry information is limited or of low quality, because there is insufficient time for learning to correct the biases that lead to mistakes. 本节的结果与上一节的结果对比，凸显了在决策协议中引入偏差的影响。当参与者存在多种偏差时，买断（buyout）能产生最佳表现，这是因为不可逆的错误非进入（nonentry）成本远高于可通过退出（exit）纠正的错误进入成本。这使得悲观团队通过合作组织时比乐观团队通过买断组织时更具破坏性；因此，当参与者围绕中性偏差对称分布时，买断是更稳健的决策结构。此外，当进入前信息有限或质量较低时，合作会产生特别差的表现，因为没有足够的时间通过学习来纠正导致错误的偏差。

Comparison of Decision-Making Structures with Populations of Biased Agents

具有偏置代理群体的决策结构比较

In our computational model, with equal opportunity costs, partnership generates the best results when all prospective entrepreneurs are unbiased (Bayesian-rational), whereas buyout generates the best results when prospective entrepreneurs have a range of biases but remain unbiased on average. We next turn to an examination of relative outcomes when agents come from a distribution that exhibits bias on average. Here, our focus is on understanding the conditions under which buyout dominates partnership. 在我们的计算模型中，在机会成本相等的情况下，当所有潜在创业者都无偏（贝叶斯理性）时，合作能产生最佳结果；而当潜在创业者存在一定程度的偏差但总体上无偏时，收购能产生最佳结果。接下来，我们考察当代理（创业者）来自总体存在偏差的分布时的相对结果。在这里，我们的重点是理解收购优于合作的条件。

We construct nine sets of population distributions corresponding to three mean levels of initial beliefs—an optimistic population, where $\hat { p } _ { - \Lambda } \sim$ β(3,2); a realistic population, where $\hat { p } _ { - \Lambda } \sim \ \beta ( 2 , 2 )$ and a pessimistic population, where $\hat { p } _ { - \Lambda } \sim \beta ( 2 , 3 ) -$ and three mean levels of precision—an underprecise population, where $I o g \hat { \tau } / \tau \sim \beta ( 3 , 2 )$ ; a correctly precise (in aggregate) population, where $I o g \hat { \tau } / \tau \sim$ $\beta ( 2 , 2 )$ ; and an over-precise population, where $I o g \hat { \tau } / \tau \sim \beta ( 2 , 3 )$ . Figure A3 in the Appendix illustrates these nine pairs of distributions that define the estimation and confidence biases of each population under study. 我们构建了九组人口分布，对应三种初始信念均值水平——乐观群体（其中 $\hat{p}{-\Lambda} \sim \beta(3,2)$）、现实群体（其中 $\hat{p}{-\Lambda} \sim \beta(2,2)$）和悲观群体（其中 $\hat{p}_{-\Lambda} \sim \beta(2,3)$）——以及三种精度均值水平——精度不足群体（其中 $\text{log}\hat{\tau}/\tau \sim \beta(3,2)$）、精度正确（总体层面）群体（其中 $\text{log}\hat{\tau}/\tau \sim \beta(2,2)$）和精度过高群体（其中 $\text{log}\hat{\tau}/\tau \sim \beta(2,3)$）。附录中的图 A3 展示了这九组分布对，它们定义了每个研究群体的估计偏差和置信偏差。

Figure 7 depicts the boss and buyout profits relative to partnership across these nine types of populations with $\Lambda$ ranging from 0.1 to 5. The left and center panels of Figure 7 show that, when agents are drawn from underestimating (pessimistic) or correctly estimating (realistic) populations, buyout 图7描绘了这九类人群中，相对于合伙制的老板利润和收购利润，其中Λ的取值范围为0.1到5。图7的左侧和中间面板显示，当参与者来自低估（悲观）或正确估计（现实）人群时，收购

FIGURE 7 The Optimal Decision-Making Structure in a Biased Population Depends on Bias and Pre-Entry Learning Duration 图7 有偏群体中的最优决策结构取决于偏差和事前学习时长

-kula $\left( \Lambda \right)$ .“Underestimation,” $\log _ { 2 } \beta ( 2 , 3 )$ , $\log _ { 2 } \beta ( 2 , 2 )$ , and $\log _ { 2 } \beta ( 3 , 2 )$ , respectively. For example, when the population is, on average, underprecise and the initial probability of success is underestimated (i.e., top-left panel), performance under buyout is, on average, ${ \sim } 5 0 %$ better than performance under partnership for a pre-entry learning duration of $\Lambda = 2$ A log-scale is applied to the $\mathbf { x }$ axis. -kula $\left( \Lambda \right)$ .“低估”，$\log _ { 2 } \beta ( 2 , 3 )$，$\log _ { 2 } \beta ( 2 , 2 )$，以及 $\log _ { 2 } \beta ( 3 , 2 )$，分别如此。例如，当总体平均而言不够精确，且初始成功概率被低估时（即左上角面板），在预进入学习时长为 $\Lambda = 2$ 的情况下，买断方案的表现平均比合作方案好约 50%。x 轴采用对数刻度。

delivers higher average performance than boss or partnership, regardless of the precision biases of the population. delivers higher average performance than boss or partnership, regardless of the precision biases of the population.

In overestimating (optimistic) populations, however, the patterns are more intriguing. When preentry learning is very limited, buyout provides the best structure. By contrast, with ample pre-entry learning, partnership becomes the best structure. 然而，在高估（乐观）人口的情况下，模式更为耐人寻味。当进入前学习非常有限时，收购提供了最佳结构。相比之下，当存在大量的进入前学习时，合作成为最佳结构。

This is depicted by the buyout and boss lines falling below zero for modest levels of $\Lambda$ in the rightmost panels. Although initial optimism in the population promotes entry for all structures, thereby limiting the overall incidence of mistaken nonentry, the “AND” structure of partnership additionally reduces the relative incidence of mistaken entry so long as the agents have had enough learning to overcome their initial biases. Figure 8 depicts this dynamic: while the cost of mistaken entry does not change much for buyout as $\Lambda$ increases (Panel A), it falls precipitously for partnership (Panel B). When prospective entrepreneurs are drawn from a population that is optimistic, then “two heads are better than one” in partnership, as its “AND” structure limits mistaken entry that would otherwise occur under boss or buyout with one overly optimistic agent. In fact, partnership’s relative advantage is greatest when agents display both initial overestimation and overprecision (see bottom right panel of Figure 7). In this case, partnership generates the best of both worlds, with optimism reducing nonentry mistakes and overprecision limiting the partnership’s propensity to make exit mistakes (partnerships are vulnerable to exit mistakes because exit is triggered by the agent with the smaller belief $\hat { \boldsymbol p } _ { t } ]$ . This is depicted by the buyout and boss lines falling below zero for modest levels of $\Lambda$ in the rightmost panels. Although initial optimism in the population promotes entry for all structures, thereby limiting the overall incidence of mistaken nonentry, the “AND” structure of partnership additionally reduces the relative incidence of mistaken entry so long as the agents have had enough learning to overcome their initial biases. Figure 8 depicts this dynamic: while the cost of mistaken entry does not change much for buyout as $\Lambda$ increases (Panel A), it falls precipitously for partnership (Panel B). When prospective entrepreneurs are drawn from a population that is optimistic, then “two heads are better than one” in partnership, as its “AND” structure limits mistaken entry that would otherwise occur under boss or buyout with one overly optimistic agent. In fact, partnership’s relative advantage is greatest when agents display both initial overestimation and overprecision (see bottom right panel of Figure 7). In this case, partnership generates the best of both worlds, with optimism reducing nonentry mistakes and overprecision limiting the partnership’s propensity to make exit mistakes (partnerships are vulnerable to exit mistakes because exit is triggered by the agent with the smaller belief $\hat { \boldsymbol p } _ { t } ]$ .

FIGURE 8 Why Partnership Overtakes Buyout in Overestimating Populations When Pre-Entry Learning Is Sufficiently Long
图8 当进入前学习足够长时，合作优于收购以高估种群数量的原因

o sion drawn from a $\log _ { 2 } \beta ( 2 , 2 )$ tThei tmen pro aiens. The paneica increasing $\Lambda$ from 0.1 to 1.0 in buyout reduces the losses from type $L$ teams and increases the gains from type $H$ teams modestly when agent 1’s initial beliefs are between 0.2 and 0.8. By contrast, the right panel shows that increasing $\Lambda$ from 0.1 to 1.0 in partnership substantially reduces the losses incurred by type $L$ teams when agent 1’s initial beliefs range from 0.4 to 0.9, while moderately increasing the gains from type $H$ teams when agent 1’s initial beliefs range from 0.2 through 0.6. o sion drawn from a $\log _ { 2 } \beta ( 2 , 2 )$ tThei tmen pro aiens. The paneica increasing $\Lambda$ from 0.1 to 1.0 in buyout reduces the losses from type $L$ teams and increases the gains from type $H$ teams modestly when agent 1’s initial beliefs are between 0.2 and 0.8. By contrast, the right panel shows that increasing $\Lambda$ from 0.1 to 1.0 in partnership substantially reduces the losses incurred by type $L$ teams when agent 1’s initial beliefs range from 0.4 to 0.9, while moderately increasing the gains from type $H$ teams when agent 1’s initial beliefs range from 0.2 through 0.6.

Our results, then, show that, although buyout handles populations with distributions of biases effectively, its advantage disappears when populations display sufficient optimism bias about their projects’ likelihood of success. For optimistic populations—and especially optimistic, overprecise populations—the partnership structure yields the highest relative profits in expectation when pre-entry learning is sufficiently long. 因此，我们的研究结果表明，尽管收购处理能够有效应对存在偏差分布的群体，但当这些群体对自身项目的成功可能性表现出足够的乐观偏差时，收购的优势便会消失。对于乐观的群体——尤其是乐观且过度精确的群体——当进入前学习的时间足够长时，合作结构在预期中能带来最高的相对利润。

Selection, Observed Bias, and Post-Entry Performance

选择、观察偏差与进入后表现

The analysis in the prior section focused on total profits generated by all firms that begin the learning process. In this section, we focus our results on differences among entrants. In most empirical studies, only data about entrants will be available for analysis. We thus offer some of our model’s implications for these empirical studies. We focus on three measures—operating profits, initial estimation bias, and precision bias—and examine how they differ in the population of surviving entrants over time. Each of the measures and their correlations changes dynamically over time as a result of patterns of exit shaped by pre-entry information, agents’ biases, and decision-making structure. We return to the assumptions in “Comparison of Decision-Making Structures with a Population of Mean-Unbiased Agents” (section above) of mean-unbiased agents with equal opportunity costs, and hold $\Lambda = 1$ to examine these patterns. 上一节的分析聚焦于所有开始学习过程的企业所产生的总利润。本节我们将研究新进入者之间的差异。在大多数实证研究中，仅可获取关于新进入者的数据用于分析。因此，我们为这些实证研究提供模型的部分启示。我们关注三个指标——经营利润、初始估计偏差和精度偏差，并考察它们在存活新进入者群体中随时间的差异。由于退出模式受到进入前信息、主体偏差和决策结构的影响，每个指标及其相关性会随时间动态变化。我们回到“与无偏均值主体群体比较决策结构”（上一节）中关于机会成本相等的无偏均值主体的假设，并保持Λ=1来考察这些模式。

Entrants in our model will either take the form of a single owner or a two-owner partnership. Firms owned by a single individual may either come from the boss structure or from the buyout structure when the buyout option is exercised. Similarly, jointly owned firms come from either the partnership structure or the buyout structure when the team members enter as partners. Figure 9 plots the results over time for these four categories of entrants: two single-owner lines (boss or buyout $\longrightarrow$ boss) and two joint-owner lines (partnership and buyout $\longrightarrow$ partner). Panel A shows that, for all decision-making structures, average operating profits rise over time as (predominantly) type $L$ firms drop out of the market. Unsurprisingly, Panel A also shows that jointly owned firms generate higher operating profits than individually owned firms. This occurs because the “AND” decision-making structure reduces entry by type $L$ firms. Additionally, Panel A shows that buyout boss realizes the lowest operating profits; among these entrants, the winner’s curse is severe. Additionally, for type $L$ entrants, jointly owned firms (average time to exit $\it \Delta \phi = \Delta \phi . 5 4$ periods)exit earlier than singly owned firms (average time to exit $= ~ 6 . 3 6$ periods). While this survival prediction is consistent with the results reported in a working paper by Greenberg and Mollick (2018), the performance results are not, perhaps suggesting that the underlying distribution of opportunities examined by Greenberg and Mollick’s data set differs between individual and jointly founded firms. 参赛主体的模式将采用单一所有者或两所有者合伙制。由个人单独拥有的企业，在行使收购选择权时，可来自老板结构或收购结构。同样，联合拥有的企业要么来自合伙制结构，要么来自团队成员以合伙人身份加入时的收购结构。图9展示了这四类参赛主体随时间的结果：两条单一所有者线（老板或收购→老板）和两条联合所有者线（合伙制和收购→合伙人）。面板A显示，对于所有决策结构，平均运营利润随时间上升，因为（主要是）L型企业退出市场。不出所料，面板A还显示，联合拥有的企业比个人拥有的企业产生更高的运营利润。这是因为“与”决策结构减少了L型企业的进入。此外，面板A显示，收购老板的运营利润最低；在这些参赛主体中，赢家诅咒现象严重。此外，对于L型参赛主体，联合拥有的企业（平均退出时间Δφ = Δφ.54期）比单独拥有的企业（平均退出时间= ~6.36期）更早退出。虽然这一存活预测与Greenberg和Mollick（2018）的工作论文中报告的结果一致，但绩效结果却不一致，这可能表明Greenberg和Mollick的数据集所考察的机会基础分布在个人和联合创立的企业之间存在差异。

FIGURE 9 Temporal Dynamics of Decision-Making Structures in Surviving Entrant Populations
图9 存活进入者群体中决策结构的时间动态

Notes: $\Lambda = 1$ bution and precision is drawn from a $\log _ { 2 } \beta ( 2 , 2 )$ distribution. Opportunity costs $k _ { i } = 5 0$ for both agents across all cases. In Panels BD, the agent in whom bias is measured is the single-owner agent for buyout $\longrightarrow$ boss and boss, and (arbitrarily) agent 1 in partnership and buyout $\longrightarrow$ partner-overprecision. Panel D is the correlation between precision and estimation biases, and Panels E and $\mathrm { F }$ are the within-team correlations of estimation bias and precision bias, respectively. 注：$\Lambda = 1$ 分布和精度来自 $\log_2 \beta(2, 2)$ 分布。所有情况下，两个代理的机会成本 $k_i = 50$。在面板 BD 中，测量偏差的代理是买断中的单一所有者代理（即老板和老板），以及（任意）合伙制和买断中的代理 1（即合伙人-过度精确）。面板 D 是精度与估计偏差之间的相关性，面板 E 和 F 分别是估计偏差和精度偏差的团队内相关性。

Panels B, C, and D yield predictions about the initial estimation and precision biases likely to be held by the entrant’s owners. Panel B shows that, while the median founders of all types of structures exhibit estimation bias, founders of single-owner (boss) entrants display greater initial optimism than founders of jointly owned (partnership) entrants. Buyout boss firms’ owners are particularly optimistic. Panel C displays the median levels of precision in the populations of survivors over time. While partnership founders display slight underprecision, boss founders exhibit significant levels of overprecision, especially in periods 1 through 10 post-entry. Panel D shows the expected correlation between estimation bias and precision bias for new founders by decision-making structure. While all founders display a positive correlation between optimism and overprecision (a negative correlation between estimation and precision bias), those operating jointly owned firms display a lower degree of correlation than those operating individually owned firms. 面板B、C和D提供了关于参赛者所有者可能持有的初始估计和精度偏差的预测。面板B显示，尽管所有类型结构的中位数创始人都表现出估计偏差，但单所有者（老板）参赛者的创始人比联合所有者（合伙制）参赛者的创始人表现出更大的初始乐观主义。收购老板企业的所有者尤其乐观。面板C展示了幸存者群体随时间变化的中位数精度水平。尽管合伙制创始人表现出轻微的精度不足，但老板制创始人表现出显著的精度过度，尤其是在进入后第1至10期。面板D显示了新创始人按决策结构划分的估计偏差与精度偏差之间的预期相关性。虽然所有创始人都表现出乐观主义与精度过度之间的正相关（即估计偏差与精度偏差之间的负相关），但经营联合所有制企业的创始人之间的相关性程度低于经营个体所有制企业的创始人。

In Panels E and F, we look at the correlation between initial estimation bias and precision bias within entrepreneurial teams. By construction, the boss structure leads to no correlation between team members, as agent 2’s beliefs are irrelevant for operating the firm. Buyout $\longrightarrow$ boss, by contrast, yields negative correlations between both the estimation and precision biases of team members; in other words, when the single-owner firm is the result of a buyout, the owner is likely to be optimistic (“overprecise”), while the nonowner employee is likely to be pessimistic (“underprecise”). The partnership structure yields the opposite results. In all jointly owned entrants, whether originating via partnership or buyout, team estimation and precision biases are positively correlated across team members. Our predictions about the combinations of cognitive biases in teams complement those of Parker (2009a), are readily testable, and are, to the best of our knowledge, unique. 在面板E和F中，我们考察创业团队中初始估计偏差与精度偏差之间的相关性。根据构造，老板结构导致团队成员之间不存在相关性，因为代理人2的信念与企业运营无关。收购→老板结构则会导致团队成员的估计偏差和精度偏差均呈负相关；换句话说，当单一所有者企业是通过收购形成时，所有者可能更乐观（“过度精确”），而非所有者员工可能更悲观（“精度不足”）。合伙制结构则产生相反的结果。在所有共同拥有的新进入者中，无论通过合伙制还是收购形成，团队成员之间的估计偏差和精度偏差均呈正相关。我们关于团队中认知偏差组合的预测补充了Parker（2009a）的研究，且易于检验，据我们所知，这些预测具有独特性。

Finally, we note the differential entry patterns that result under our assumptions in this section. Among firms starting out as boss, $5 8 . 0 %$ enter the market and $4 3 . 5 %$ of these are still in operation after 5 periods. For partnership, the figures are $3 5 . 2 %$ and $2 5 . 6 %$ , respectively. Teams that begin with buyout enter the market $8 0 . 5 %$ of the time, of which $4 3 . 8 %$ enter as partnerships and $5 6 . 2 %$ enter as boss firms. Collectively, the entry and persistence dynamics that we model offer some insight into the relative paucity of partnerships in reality, as highlighted in the introduction. Conditional on equal numbers of teams beginning the pre-entry learning process in boss, partnership, and buyout decision-making structures, partnerships will represent a minority of the entrants. 最后，我们注意到在本节的假设下出现的差异化进入模式。在以“老板”模式起步的企业中，有58.0%进入市场，其中43.5%在5个周期后仍在运营。对于合伙制，相应的数字分别为35.2%和25.6%。以收购起步的团队有80.5%的概率进入市场，其中43.8%以合伙制形式进入，56.2%以“老板”企业形式进入。总体而言，我们所建模的进入和存续动态为现实中合伙制相对稀缺的现象提供了一些见解，这一点在引言中已强调。在开始前进入学习阶段的团队在“老板”、合伙制和收购决策结构中数量相等的情况下，合伙制将占进入者的少数。

（注：原文中的“boss”“partnership”“buyout”等为模式名称，保留原样；数字格式按原文处理，如“5 8 . 0 %”保留空格及格式，翻译时合并为“58.0%”）

Finding the Optimal Decision-Making Structure for Teams with Known Bias

为存在已知偏见的团队寻找最优决策结构

The prior sections examined the relative performance of boss, partnership, and buyout decisionmaking structures on the expected profits of populations of agents with varying characteristics, as well as the selection impact of decisionmaking structure on performance and bias characteristics of entrants and survivors in the marketplace. We next turn to a more prescriptive analysis by asking: “Given two agents with known bias characteristics, which decision-making structure maximizes the expected profits for their venture?” The purpose of this prescriptive analysis is to suggest an optimal matching of decision-making structure to entrepreneurs’ biases when these confidence biases are known. 前几节研究了老板制、合伙制和买断制这三种决策结构对具有不同特征的代理人群体预期利润的相对表现，以及决策结构对市场中进入者和幸存者的表现及偏差特征的选择影响。接下来，我们转向更具规范性的分析，提出这样一个问题：“给定两个具有已知偏差特征的代理，哪种决策结构能使他们的项目预期利润最大化？”这种规范性分析的目的是在创业者的信心偏差已知的情况下，建议决策结构与创业者偏差的最优匹配。

Figure 10 displays the optimal decision-making structure for each pair of agents with varying levels of estimation and precision bias and $\Lambda = 1$ .The yellow region depicts where buyout delivers the highest expected profits, the blue region where boss delivers the highest expected profits, and green indicates where partnership delivers the highest expected profits. The center block of the central panel provides the optimal decision-making structure for unbiased-Bayesian agents, which is partnership. Focusing on the central panel, where precision biases are absent, partnership generates better results when agents’ initial beliefs are positively biased on average, and, conversely, buyout generates better results when agents’ initial beliefs are negatively biased on average. The results here are intuitive: the “AND” structure of partnership corrects agents’ optimism by making both agents’ agreement a necessary condition for entry. Buyout option, by contrast, counteracts agents’ pessimism by requiring the assent of only one agent to enter. Furthermore, we also observe, in this central panel, that, if both agents have large and opposite estimation biases, the profit-maximizing structure is boss. In other words, in absence of precision bias, boss generates the highest value only if the extreme and opposite estimation biases of the agents make both partnership and buyout highly ineffective. 图10展示了每对具有不同估计水平和精度偏差且$\Lambda = 1$的代理的最优决策结构。黄色区域表示买断能带来最高预期利润，蓝色区域表示老板（boss）能带来最高预期利润，绿色表示合作（partnership）能带来最高预期利润。中央面板的中心块提供了无偏贝叶斯代理的最优决策结构，即合作。聚焦于中央面板（此处无精度偏差），当代理的初始信念平均呈正偏差时，合作产生更好的结果；相反，当代理的初始信念平均呈负偏差时，买断产生更好的结果。这里的结果很直观：合作的“与”结构通过使双方达成协议成为进入的必要条件，纠正了代理的乐观情绪。相比之下，买断选项通过仅要求一名代理同意即可进入，抵消了代理的悲观情绪。此外，在该中央面板中，我们还观察到，如果两个代理都有较大且相反的估计偏差，利润最大化的结构是老板。换句话说，在无精度偏差的情况下，只有当代理的极端且相反的估计偏差使合作和买断都非常无效时，老板才会产生最高价值。

Moving beyond the central panel, we observe that the optimal decision-making structure for a pair of agents changes as we introduce their precision biases in addition to biases in estimation. Our prior work at the individual level shows that the severity of impact of an estimation bias depends on the precision bias (Chen et al., 2018). Underprecision reduces the severity of initial estimation bias (either positive or negative), whereas overprecision exacerbates the severity of initial estimation bias, especially when agents are overly optimistic. These asymmetries, along with decision-making structure, shape the remaining patterns in Figure 10. Across most 超越中央面板，我们观察到，当我们在 estimators 的偏差之外引入代理人的精度偏差时，一对代理人的最优决策结构会发生变化。我们在个体层面的先前工作表明，估计偏差的影响严重程度取决于精度偏差（Chen et al., 2018）。精度不足会降低初始估计偏差（无论是正偏差还是负偏差）的严重程度，而精度过高会加剧初始估计偏差的严重程度，尤其是当代理人过于乐观时。这些不对称性以及决策结构共同塑造了图10中剩余的模式。在大多数情况下

FIGURE 10 Optimal Decision-Making Structure as a Function of Both Estimation and Precision Biases
图10 作为估计偏差和精度偏差函数的最优决策结构

Agent 2 Precision Agent 2 精度

NoeEa plotisplhetadcin-makircu heplicable, preen $\Lambda = 1$ at specified values of estimation and precision biases. The larger $9 \times 9$ grid varies precision bias from overprecise to underprecise values for agent 1 (vertical, bottom to top) and agent 2 (horizontal, left to right). Each smaller $9 \times 9$ grid varies the estimation bias from underestimated to overestimated values ple, if agent 1 is overprecise and overestimates the initial probability of success (lower rows of larger $9 \times 9$ , upper rows of smaller $9 \times 9 s$ and $9 \times 9$ , rows toward the left of smaller $9 \times 9 \mathrm { s }$ ), then buyout is likely to be the optimal decision-making structure (i.e., lower right of larger $9 \times 9$ , upper left of smaller $9 \times 9 s$ are mostly structures. NoeEa plotisplhetadcin-makircu heplicable, preen $\Lambda = 1$ at specified values of estimation and precision biases. The larger $9 \times 9$ grid varies precision bias from overprecise to underprecise values for agent 1 (vertical, bottom to top) and agent 2 (horizontal, left to right). Each smaller $9 \times 9$ grid varies the estimation bias from underestimated to overestimated values ple, if agent 1 is overprecise and overestimates the initial probability of success (lower rows of larger $9 \times 9$ , upper rows of smaller $9 \times 9 s$ and $9 \times 9$ , rows toward the left of smaller $9 \times 9 \mathrm { s }$ ), then buyout is likely to be the optimal decision-making structure (i.e., lower right of larger $9 \times 9$ , upper left of smaller $9 \times 9 s$ are mostly structures.

combinations of precision bias, partnership tends to be the optimal structure when both agents have initial optimism, and buyout option tends to be the optimal structure when both agents have initial pessimism. Interestingly, the region in which buyout option dominates grows when at least one agent has underprecision bias; it remains relatively fixed when both agents have overprecision bias. Underprecision makes individuals’ beliefs more likely to fall below $p ^ { * }$ , which in turn differentially makes partnerships more likely to commit exit mistakes, since a single agent’s withdrawal of support terminates the operation. Finally, when both agents have strong, but opposing, underand overprecision biases, boss is more likely to dominate. When team members draw very different conclusions based on the same data (i.e., place very different weights on new information), then joint decision-making becomes ineffective, and it may simply be better to ignore one agent’s perspective. 当双方代理人初始都持乐观态度时，精确偏差的组合下，合作关系往往是最优结构；当双方初始都持悲观态度时，收购选择权往往是最优结构。有趣的是，至少有一方代理人存在精度不足偏差时，收购选择权占优的区域会扩大；当双方都存在精度过剩偏差时，该区域相对固定。精度不足会使个体的信念更可能低于 \( p^* \)，进而导致合作关系更可能出现退出失误（因为单个代理人撤回支持会终止合作）。最后，当双方代理人都存在强烈但相反的精度不足和精度过剩偏差时，老板（或主导方）更可能占优。当团队成员基于相同数据得出截然不同的结论（即对新信息赋予的权重差异很大）时，联合决策会失效，此时可能更好的做法是忽略某一方的观点。

We expand upon these implications of these observations for improving decision-making in the early stages entrepreneurship in the discussion below. Our insights complement traditional policies to address bias among entrepreneurs, which involve screening out highly biased individuals, de-biasing them through information and education, or structuring their learning processes. We posit that structure should follow bias. Specifically, our model suggests that, when individuals’ confidence biases are known, but are difficult or costly to correct, entrepreneurs should carefully select a decision-making structure that serves best to mitigate their biases. 我们在下文讨论中进一步阐述这些观察结果对改善早期创业阶段决策的影响。我们的见解补充了传统政策，以解决创业者中的偏见问题，这些政策包括筛选出高度有偏见的个人、通过信息和教育对其进行去偏，或构建其学习过程。我们认为结构应遵循偏见。具体而言，我们的模型表明，当个人的信心偏见已知但难以或成本高昂地纠正时，创业者应仔细选择最能减轻其偏见的决策结构。

Boundary Conditions and Limitations

边界条件与限制

Our model is a computational model rather than an analytical one, and we exercise it using a fixed set of parameters. We do not claim that our results hold for all possible values of these parameters, $p$ ,μH, μL, σ, and δ. We note, however, these parameters were chosen specifically to make the signal extraction problem in the model as difficult as possible—there is an equal ex ante likelihood of success and failure, and the magnitudes of the high and low signals are equal. Holding these assumptions fixed, in unreported work, we vary noise, $\mathbf { \sigma } ^ { \sigma ^ { 2 } }$ , by a factor of four in either direction; the results remain qualitatively the same. Other changes to our parameters would make the signal extraction problem fundamentally easier (see Ryan & Lippman, 2003, for intuition). To our knowledge, this would not change the relative performance of the decisionmaking structures analyzed herein. 我们的模型是一个计算模型而非分析模型，我们使用固定的参数集来运行它。我们并不声称我们的结果适用于这些参数（\( p \)、\( \mu_H \)、\( \mu_L \)、\( \sigma \) 和 \( \delta \)）的所有可能取值。然而，我们注意到，这些参数的选择是为了使模型中的信号提取问题尽可能困难——事前成功和失败的可能性相等，且高低信号的大小相等。在保持这些假设不变的情况下，在未报告的研究中，我们将噪声 \( \mathbf{\sigma}^{\sigma^2} \) 向任一方向调整四倍；结果在质量上保持不变。对我们参数的其他更改会从根本上使信号提取问题变得更容易（有关直观理解，请参见 Ryan & Lippman, 2003）。据我们所知，这不会改变本文分析的决策结构的相对性能。

Furthermore, when we examine populations with biases, we apply a particular functional form to the distribution of biases. While we have also examined alternative distributions with greater dispersion than our main assumptions in the section titled “Comparison of Decision-Making Structures with a Population of Mean-Unbiased Agents” (see footnote 22), we cannot rule out the possibility that other distributions yield different conclusions. In “Comparison of Decision-Making Structures with Populations of Biased Agents” (also above), we explicitly focus on directly identifying the boundary conditions of our results by drawing from a series of beta distributions. Here, too, there is a possibility that alternative functional forms could yield different conclusions. 此外，当我们研究存在偏差的群体时，我们会对偏差的分布应用一种特定的函数形式。虽然我们在标题为“具有均值无偏代理群体的决策结构比较”的章节中也研究了比我们主要假设更分散的替代分布（见脚注22），但我们不能排除其他分布可能得出不同结论的可能性。在“具有偏差代理群体的决策结构比较”（同上）中，我们明确通过一系列β分布来直接确定我们结果的边界条件。同样，这里也存在其他函数形式可能得出不同结论的可能性。

Finally, we assume that the pre-entry signals of our agents are uncorrelated—that is, that the members of the entrepreneurial team learn independently about the same opportunity prior to entry. This is an assumption that we can easily relax, by introducing a correlation in the noise team members receive. When agents are deterministically unbiased, the superiority of the partnership structure is robust to pre-entry noise correlation, though of course performance of all decision-making structures collapses to the single-agent case—that is, boss—when signals are identical (because, in that case, all agents’ beliefs are identical). When agents are drawn from populations that include biases, the results remain qualitatively the same and even quantitatively similar across the full range of noise correlation, because, in this case, the results are driven not only by evolving beliefs that are affected by the correlation, but also trait-like biases that are unaffected by it. (See Figures A4-A6 in the Appendix and the associated discussion of noise correlation between agents.) 最后，我们假设我们代理的事前信号是不相关的——也就是说，创业团队成员在进入之前会独立地了解到同一个机会。我们可以通过在团队成员接收的噪声中引入相关性来轻松放松这个假设。当代理是确定性无偏的时候，合作结构的优越性对于事前噪声相关性是稳健的，尽管当然，所有决策结构的表现都会坍缩到单代理的情况——也就是老板——当信号相同时（因为在这种情况下，所有代理的信念都是相同的）。当代理来自包含偏差的群体时，结果在质量上保持相同，甚至在整个噪声相关范围内在数量上也相似，因为在这种情况下，结果不仅由受相关性影响的演化信念驱动，还由不受相关性影响的特质类偏差驱动。（见附录中的图A4-A6以及相关的关于代理之间噪声相关性的讨论。）

Our study is not, of course, without multiple limitations, of which we can only include a partial list here. For tractability, we abstract away from issues of effort and investment through which an entrepreneur can affect their prospects for success. Our model thus represents a process of passive, rather than active, learning (see Pakes & Ericson, 1998, for a discussion). Relatedly, the notion of pivoting (changing to a new idea or approach), as exemplified in recent work on lean startups (Blank, 2013; Contigiani & Levinthal, 2019; Ries, 2011), is beyond the scope of our model. Moreover, teams are known to suffer from free-riding problems, which makes outcomes particularly sensitive to the distribution of rewards ex post, which we ignore. Additionally, we ignore (a) the possibility that optimism can affect not only whether the entrepreneur exploits an opportunity, but also how that happens (e.g., Dushnitsky, 2010); (b) alternative mechanisms that lead to overconfidence, such as asymmetric updating or confirmatory bias, which has been identified as empirically important in laboratory studies of exit delay (Elfenbein et al., 2017); and (c) anchoring bias, which has been examined in survey-based work (Simon, Houghton, & Aquino, 2000). Our model is amenable to examining the impact of these and other biases, but, for simplicity, we have abstracted away from them. Furthermore, we have modeled the length of the pre-entry learning period as exogenous. Intuitively, endogenizing the entry timing against the backdrop of an opportunity that is declining in value will slow down the decision-making in a partnership relative to other structures, leading it to make fewer mistakes of all kinds. The net impact of this delay would depend critically on whether the partners face a single opportunity or a series of them. We believe that these interactions and extensions will provide fertile ground for future work. 当然，我们的研究存在诸多局限性，此处仅能列举部分。为便于处理，我们抽象掉了创业者可通过其影响成功前景的努力和投入问题。因此，我们的模型代表的是一种被动而非主动的学习过程（关于这一点，可参考Pakes & Ericson，1998年的讨论）。同样，近期关于精益创业的研究（Blank，2013；Contigiani & Levinthal，2019；Ries，2011）中所体现的“转型”（即转向新想法或新方法）概念，也超出了我们模型的研究范围。此外，团队众所周知会存在搭便车问题，这使得结果对事后奖励分配极为敏感，而我们对此未作考虑。另外，我们忽略了以下几点：(a) 乐观情绪不仅会影响创业者是否利用机会，还会影响其利用机会的方式（例如，Dushnitsky，2010）；(b) 导致过度自信的其他机制，如不对称更新或确认偏差，这在实验室研究的退出延迟中被证实具有重要的实证意义（Elfenbein等人，2017）；以及(c) 锚定效应，这一点在基于调查的研究中已有考察（Simon、Houghton & Aquino，2000）。我们的模型可以用来研究这些及其他偏差的影响，但为简化起见，我们已将其抽象掉。此外，我们将进入前学习期的长度建模为外生变量。直观上，在机会价值下降的背景下内生决定进入时机，与其他结构相比，会减缓合作关系中的决策过程，使其减少各类错误。这种延迟的净影响将关键取决于合作伙伴面临的是单一机会还是一系列机会。我们相信，这些互动和扩展将为未来的研究提供丰富的基础。

CONCLUSION AND DISCUSSION

结论与讨论

New ventures are commonly founded by teams of entrepreneurs, who must employ a decision-making structure that implicitly or explicitly defines how individual beliefs are aggregated into team decisions. How should decision-making be organized in entrepreneurial teams when founders exhibit confidence biases? We extend Chen et al. (2018)’s computational model of entrepreneurial learning by (potentially) biased agents to include multiple team members who aggregate beliefs and make choices about entry and exit based upon different decisionmaking structures. We build on the work of Sah and Stiglitz (1986), Christensen and Knudsen (2010), and Csaszar (2013) in comparing the performance of structures in which all agents must agree to market entry and continuation decisions (partnership) to structures in which the affirmation of only one agent may be required to enter or exit the market (boss and buyout). Our model allows us to identify both the optimal decision-making structure when the estimation and precision biases of the team members are known ex ante and the relative performance of the different decision-making structures when the ex ante biases are unknown, but are drawn from known distributions. 新企业通常由创业团队创立，这些团队必须采用一种决策结构，该结构隐性或显性地定义了个体信念如何汇总为团队决策。当创始人表现出信心偏差时，创业团队中的决策应如何组织？我们将Chen等人（2018）提出的具有（潜在的）偏差代理的创业学习计算模型扩展到包括多个团队成员，这些成员基于不同的决策结构汇总信念并做出进入和退出市场的选择。我们借鉴Sah和Stiglitz（1986）、Christensen和Knudsen（2010）以及Csaszar（2013）的研究，比较两种决策结构的绩效：一种是所有代理必须就市场进入和持续决策达成一致（伙伴制），另一种是仅需一名代理确认即可进入或退出市场（老板制和买断制）。当团队成员的估计和精确性偏差在事前已知时，我们的模型能够确定最优决策结构；当事前偏差未知但来自已知分布时，模型可比较不同决策结构的相对绩效。

We find that the strength of equal partnership voting in two-person teams is in handling prospective entrepreneurs who are biased in the sense that they initially overestimate their likelihood of success. A buyout option can create value by enabling the team to deal with an agent who has a pessimistic viewpoint or an idiosyncratically high opportunity cost, either of which, in the absence of a buyout option, can prevent profitable ventures from getting off the ground. At the same time, the buyout option also carries with it the winner’s curse. Its net impact, as we have shown, is a function of both estimation and precision biases as well as the quality of pre-entry learning. 我们发现，在两人团队中，平等伙伴投票的优势在于应对那些存在偏见的潜在创业者——这类创业者最初会高估自己的成功可能性。收购选择权可以创造价值，因为它能让团队应对持悲观观点或具有特殊高机会成本的代理人；若没有收购选择权，这两种情况都可能使盈利项目无法启动。同时，收购选择权也存在“赢家诅咒”。正如我们所表明的，其净影响取决于估计偏差、精确性偏差以及进入前学习的质量。

A key contribution of this study is that it unpacks the determinants of effective decision-making for entrepreneurial teams. When agents are behaviorally biased, there is not a “one size fits all” solution. Rather, the appropriate decision-making structure for the entrepreneurial venture is contingent on the nature and distribution of potential founders’ biases. 本研究的一个关键贡献在于揭示了创业团队有效决策的决定因素。当决策者存在行为偏差时，并不存在“一刀切”的解决方案。相反，创业企业适当的决策结构取决于潜在创始人偏差的性质和分布。

Our work connects with recent studies that explore decision-making in early-stage entrepreneurship (e.g., Bennett & Chatterji, 2019; Cohen, Bingham, & Hallen, 2019) and contributes to an important ongoing effort to find effective solutions for reducing decision-making errors therein. The empirical work of Camuffo et al. (2020) suggested that entrepreneurs who rigorously test their expectations/hypotheses would be less likely to pursue projects with false-positive returns. The lean startup approach (e.g., Blank, 2013; Contigiani & Levinthal, 2019; Ries, 2011) emphasizes reducing the costs of decision-making errors. Other approaches to reduce these errors include screening out entrepreneurs whose biases make them most prone to mistakes (e.g., Elfenbein et al., 2017; Gutierrez et al., 2020), providing clear information about success rates (Shane, 2008) and market noise (Elfenbein & Knott, 2015) to speed and improve the accuracy of the learning process, and suggestions from the practitioner literature for de-biasing processes (Lovallo & Sibony, 2010; Shepherd & Patzelt, 2017). By contrast, the model we develop suggests that—for entrepreneurial teams at least—careful attention to decision-making structure, potentially matched to knowledge of team members’ biases, together with conscious decisions about gathering pre-entry information can reduce costly decision-making errors in early-stage entrepreneurship. As such, our work offers a remedy when other de-biasing processes are ineffective. Future research may continue to contribute toward a richer variety of solutions for minimizing decision-making errors in the face of bias. Additionally, our model recommends extending a pre-entry learning phase to address bias and offers a lens through which to examine the work of Leatherbee and Katila (2020), who examined differences in how teams that may or may not include management experts seek out and process information about uncertain new ventures. 我们的研究与近期探索早期创业决策的研究相关（例如Bennett & Chatterji, 2019；Cohen, Bingham, & Hallen, 2019），并致力于为减少其中决策错误寻找有效解决方案的重要持续工作做出贡献。Camuffo等人（2020）的实证研究表明，严格检验自身预期/假设的创业者，不太可能追求具有假阳性回报的项目。精益创业方法（例如Blank, 2013；Contigiani & Levinthal, 2019；Ries, 2011）强调降低决策错误的成本。其他减少这些错误的方法包括筛选出因偏见而最容易犯错的创业者（例如Elfenbein et al., 2017；Gutierrez et al., 2020），提供关于成功率（Shane, 2008）和市场噪音（Elfenbein & Knott, 2015）的清晰信息以加快并提高学习过程的准确性，以及来自从业者文献的去偏过程建议（Lovallo & Sibony, 2010；Shepherd & Patzelt, 2017）。相比之下，我们开发的模型表明——至少对于创业团队而言——仔细关注决策结构（可能与团队成员偏见的知识相匹配），以及有意识地决定收集进入前信息，可以减少早期创业中代价高昂的决策错误。因此，当其他去偏过程无效时，我们的研究提供了一种补救方法。未来的研究可能会继续为在存在偏见的情况下减少决策错误提供更多样化的解决方案。此外，我们的模型建议延长进入前学习阶段以应对偏见，并提供了一个视角来审视Leatherbee和Katila（2020）的研究，他们研究了可能包含或不包含管理专家的团队如何寻求和处理关于不确定新企业的信息的差异。

Our modeling approach speaks to the literature exploring the nuances of confidence biases (e.g., Moore & Healy, 2008), and how different sources of bias affect entry in general (e.g., Du, Li, & Wu, 2019) or entrepreneurial entry specifically (e.g., Gutierrez et al., 2020). The model we develop takes into account the connected influences of estimation and precision biases as well as pre-entry learning on entry, exit, and performance implications of founding teams. In thinking specifically about how heterogeneous beliefs are aggregated into team decisions, our work is connected to studies of knowledge aggregation within teams (e.g., Taylor & Greve, 2006) as well as behavioral strategy more generally (Levinthal, 2011; Powell, Lovallo, & Fox, 2011). 我们的建模方法与探索置信偏差细微差别的文献（例如Moore & Healy，2008）以及不同偏差来源如何影响一般进入（例如Du, Li, & Wu，2019）或创业进入（例如Gutierrez等人，2020）的研究相关。我们开发的模型考虑了估计偏差和精确性偏差的相互影响，以及进入前学习对创始团队的进入、退出和绩效影响。在具体思考异质信念如何被汇总为团队决策时，我们的研究与团队内知识汇总的研究（例如Taylor & Greve，2006）以及更广泛的行为战略研究（Levinthal，2011；Powell, Lovallo, & Fox，2011）相关联。

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Daniel W. Elfenbein (elfenbein@wustl.edu) is Professor of Organization and Strategy, and Associate Dean EMBA-Shanghai, at Washington University in St. Louis. He received his PhD in business economics from Harvard University. His research focuses on how firms and employees create and capture value through reputations and relationships, on entrepreneurship, and on corporate social responsibility. 丹尼尔·W·埃尔芬贝恩（elfenbein@wustl.edu）是圣路易斯华盛顿大学组织与战略学教授，同时担任上海高级工商管理硕士项目（EMBA-Shanghai）副主任。他拥有哈佛大学商业经济学博士学位。其研究重点包括企业和员工如何通过声誉与关系创造和获取价值、创业以及企业社会责任。

Hart E. Posen (hposen@wisc.edu) is the Richard G. and Julie J. Diermeier Professor in Business at the University of Wisconsin-Madison. He received his PhD from the Wharton School, after a career as an entrepreneur in the technology and retail sectors. He studies strategy, innovation, and entrepreneurship from a behavioral perspective that focuses on the role of organizational learning. 哈特·E·波森（hposen@wisc.edu）是威斯康星大学麦迪逊分校理查德·G·和朱莉·J·迪尔迈尔商学院教授。他在科技和零售行业经历了一段创业生涯后，从沃顿商学院获得博士学位。他从行为学角度研究战略、创新和创业，该视角侧重于组织学习的作用。

Ming zhu Wang (mingzhu@wustl.edu) is a PhD candidate in strategy and entrepreneurship at Washington University in St. Louis. Her research interests are in entrepreneurship and changes in the competitive landscape. She applies experience from her prior work as a mathematician to her current research. 王明珠（mingzhu@wustl.edu）是圣路易斯华盛顿大学战略与创业方向的博士生。她的研究兴趣在于创业以及竞争格局的变化。她将之前作为数学家的工作经验应用到当前研究中。

APPENDIX

附录

ADDITIONAL RESULTS

附加结果

Profit split in proportion to opportunity costs

按机会成本比例分配利润

Figure A1 shows an alternative rule, applicable to each decision-making structure, in which profit is split in proportion to opportunity costs. As the figure shows, profit is invariant to opportunity cost split under this rule. 图A1展示了另一种规则，适用于每个决策结构，其中利润按机会成本的比例分配。如图所示，根据该规则，利润与机会成本分配无关。

John S. Chen (john.chen@warrington.ufl.edu) is Assistant Professor of Strategy at the University of Florida. John obtained his PhD from the University of Michigan. His research applies an organizational learning lens to entrepreneurship, real options, and technology standards. John employs both traditional empirical approaches and computational methods in his work.
约翰·S·陈（john.chen@warrington.ufl.edu）是佛罗里达大学战略学助理教授。约翰在密歇根大学获得博士学位。他的研究将组织学习视角应用于创业、实物期权和技术标准领域。约翰在工作中同时采用传统实证方法和计算方法。

FIGURE A1 Profit under a Partnership Rule That Splits Profits in Proportion to Opportunity Costs 图A1 按机会成本比例分配利润的合伙制下的利润情况

Notes: For $\Lambda \ : = \ : 0 . 5$ , we plot the average performance under each decision-making structure as a function of the proportion of the total opportunity costs assumed by agent 1. Here, profits are assumed to be split in proportion to opportunity costs. Total opportunity costs of entry for both agents in all simulations equal 100. The x-axis represents the proportion of total entry costs possessed by agent 1. For example, at $\mathbf { x } = \mathbf { 0 . 3 }$ , agent 1’s opportunity cost is $k _ { 1 } = 3 0$ and agent $_ 2$ ’s opportunity cost is $k _ { 2 } = 7 0$ . 注：对于 $\Lambda := 0.5$，我们将每个决策结构下的平均表现作为代理1承担的总机会成本比例的函数进行绘制。此处假设利润按机会成本比例分配。所有模拟中两个代理的总进入机会成本均为100。x轴表示代理1拥有的总进入成本比例。例如，当 $\mathbf{x} = \mathbf{0.3}$ 时，代理1的机会成本为 $k_1 = 30$，代理2的机会成本为 $k_2 = 70$。

DISTRIBUTIONS OF BIAS IN MODELED POPULATIONS

模型化人群中的偏差分布

Figures A2 and A3 show the probability density functions for the distributions used in the main paper. 图A2和图A3展示了主文中所用分布的概率密度函数。

FIGURE A2 Estimation and Precision Bias Under $\pmb { \beta }$ and Log $\pmb { \beta }$ Distributions 图A2 在±β和对数±β分布下的估计与精度偏差

Notes: The left panel plots a $\scriptstyle \left{ 3 \left( 2 , 2 \right) \right.$ probability density function as the on-average-unbiased population distribution for the initial estimation bias. The function is centered on $\hat { p } _ { - \Lambda } = 0 . 5$ t $\hat { p } _ { - \Lambda } \epsilon$ (0.5, 1) denote overestimation bias (i.e., optimism), while $\hat { p } _ { - \Lambda } \epsilon$ (0, 0.5) denotes underestimation bias (i.e., pessimism). The right panel plots a $\log _ { 2 } \beta ( 2 , 2 )$ probability density function as the on-average-unbiased population distribution for precision bias. Thefunction iscentered on $\hat { \tau } / \tau = 1$ (i.e., $\hat { \tau } / \tau = 2 ^ { \mathrm { x } }$ when $\mathbf { x } = \mathbf { 0 }$ , the unbiased value for precision. For any $\mathbf { x } \in \left( 0 , \infty \right)$ , we note that $\hat { \tau } / \tau = 2 ^ { \mathrm { x } }$ reflects as much underprecision as $\hat { \tau } / \tau = 2 ^ { - \mathbf { X } }$ reflects overprecision. The $\log _ { 2 } \beta ( 2 , 2 )$ probability density function is produced by translating each $\left( \mathbf { x } , \mathbf { y } \right)$ from the β(2,2) probability density function (left panel) to $( 2 ^ { ( \mathrm { x } \mathrm { ~ - ~ } 0 . 5 ) \cdot 5 } , \mathrm { y } )$ 注：左侧面板绘制了一个$\scriptstyle \left{ 3 \left( 2 , 2 \right) \right.$概率密度函数，作为初始估计偏差的平均无偏总体分布。该函数以$\hat { p } _ { - \Lambda } = 0 . 5$为中心，$\hat { p } _ { - \Lambda } \in (0.5, 1)$表示高估偏差（即乐观），而$\hat { p } _ { - \Lambda } \in (0, 0.5)$表示低估偏差（即悲观）。右侧面板绘制了一个$\log _ { 2 } \beta ( 2 , 2 )$概率密度函数，作为精度偏差的平均无偏总体分布。该函数以$\hat { \tau } / \tau = 1$为中心（即当$\mathbf { x } = \mathbf { 0 }$时，$\hat { \tau } / \tau = 2 ^ { \mathrm { x } }$，这是精度的无偏值）。对于任何$\mathbf { x } \in \left( 0 , \infty \right)$，我们注意到$\hat { \tau } / \tau = 2 ^ { \mathbf { x } }$反映了与$\hat { \tau } / \tau = 2 ^ { - \mathbf { x } }$相同程度的欠精度和过精度。$\log _ { 2 } \beta ( 2 , 2 )$概率密度函数是通过将β(2,2)概率密度函数（左侧面板）中的每个$\left( \mathbf { x } , \mathbf { y } \right)$转换为$( 2 ^ { ( \mathrm { x } - 0 . 5 ) \cdot 5 } , \mathrm { y } )$得到的。

FIGURE A3 Distributions from Which Agent Biases Are Drawn

图A3 代理偏差来源的分布

tially overestimates the probability of success. The $\log _ { 2 } \beta ( 2 , 3 )$ and $\log _ { 2 } \beta ( 3 , 2 )$ probability density functions reflect biased population that is (on average) underprecise. Each $\log _ { 2 } \beta$ (a, b) probability density function is produced by translating each $\left( \mathbf { x } , \mathbf { y } \right)$ from the corresponding $( 2 ^ { ( \mathrm { x \hat { \cdot } 0 . 5 } ) \cdot 5 } ,$ $\beta ( { \mathrm { a } } , { \mathrm { b } } )$ ing $\boldsymbol { \mathfrak { j } } \log _ { 2 } \ \beta ( \mathbf { a } , \mathbf { b } )$ panel. tially overestimates the probability of success. The $\log _ { 2 } \beta ( 2 , 3 )$ and $\log _ { 2 } \beta ( 3 , 2 )$ probability density functions reflect biased population that is (on average) underprecise. Each $\log _ { 2 } \beta$ (a, b) probability density function is produced by translating each $\left( \mathbf { x } , \mathbf { y } \right)$ from the corresponding $( 2 ^ { ( \mathrm { x \hat { \cdot } 0 . 5 } ) \cdot 5 } ,$ $\beta ( { \mathrm { a } } , { \mathrm { b } } )$ ing $\boldsymbol { \mathfrak { j } } \log _ { 2 } \ \beta ( \mathbf { a } , \mathbf { b } )$ panel.

CORRELATED NOISE TERMS

相关噪声术语

Next, we present the results robustnes analysis conducted t cnfirm that the key results the pap roust al corelation betwee member anentrepreneurial team ee Figure4). We begi wiueult that partnership is superior to buyout when agents are deterministically unbiased. Notice that, as one might e, th esl weaken cnderabl the celati—ah alu tecoelati pe, all structures become functionally equivalent to boss, since beliefs of all team members become identical. 接下来，我们展示稳健性分析的结果（该结果证实了论文中关键结果：成员与创业团队之间的核心相关性（见图4））。我们认为，当代理人具有确定性无偏性时，合作优于收购。注意，正如人们可能预期的那样，随着层次结构的减弱（即所有结构的相关性降低），所有结构在功能上都等同于层级结构，因为所有团队成员的信念趋于一致。

FIGURE A4 Performance Relative to Partnership Across Correlation Levels (Deterministically Unbiased Case] 图A4 在不同相关水平下的合作相对性能（确定性无偏情形）

tive to partnership performance as a function of pre-entry learning duration $\left( \Lambda \right)$ A log-scale is applied to the $\mathbf { x }$ axis. 对合作绩效的反应是前期学习时长（$\Lambda$）的函数。x轴采用对数刻度。

Interestingly, the results are much more resilient t corelation, an indeed even growtronger at low pre-ny lehentuvee,Thea thedeterminis cas whic evolving beli account or ny perormance heterogeneity across thediffent structures,differences in this case also arisfrom agent initial biases, which areinvariant to corelation. 有趣的是，结果对核心相关性的鲁棒性要高得多，实际上在低预训练权重时甚至会变得更强。这一确定的情况表明，随着信念的演变，考虑到不同结构下的性能异质性，这种差异也源于代理的初始偏差，而这些偏差与核心相关性无关。

（注：原输入存在拼写错误或乱码，如“t corelation”“growtronger”“pre-ny lehentuvee”“Thea thedeterminis cas”“perormance”“arisdfrom”等，已根据语义逻辑进行合理修正后翻译。）

修正说明：因原输入存在较多拼写错误（如“t”应为“to”、“growtronger”应为“grow stronger”、“pre-ny”应为“pre - training”、“lehentuvee”可能为“leverage”或其他术语拼写错误、“Thea thedeterminis”应为“The determining”、“perormance”应为“performance”、“arisdfrom”应为“arise from”等），为确保翻译准确性和可读性，对明显的语义错误部分进行了修正处理，以符合正常英文表达逻辑后再进行翻译。若严格按原错误拼写翻译会导致语义混乱，故此处进行合理修正。

FIGURE A5 Performance Relative to Partnership Across Correlation Levels (On Average Unbiased) 图A5 不同相关水平下相对于合作的性能（平均无偏）

tive to partnership performance as a function of pre-entry learning duration $( \Lambda )$ . Agents are, on average, unbiased with estimation drawn from a β(2,2) distribution and precision drawn from a $\log _ { 2 } \beta ( 2 , 2 )$ distribution. A log-scale is applied to the $\mathbf { x }$ axis. 对合作绩效的反应是进入前学习时长 $( \Lambda )$ 的函数。代理通常无偏，其估计值来自 $\beta(2,2)$ 分布，精度来自 $\log_2 \beta(2,2)$ 分布。对 $\mathbf{x}$ 轴应用对数刻度。

Lasa our finding that when agents are, on average, optimistic, the buyout option outperforms partnership at low peneauratonbut parehiutpeor euyutin th pre lar e.g Fgh ane he pape. Thdiigh us a eFgA. Lasa our finding that when agents are, on average, optimistic, the buyout option outperforms partnership at low penetration but partnership performs better in the early e.g. Fgh and the paper. Thdiigh us a eFgA.

tive to partnership performance as a function of pre-entry learning duration $( \Lambda )$ . Agents are, on average, optimistic with estimation drawn from a β(3,2) distribution and precision drawn from a $\log _ { 2 } \beta ( 3 , 2 )$ distribution. A log-scale is applied to the $\mathbf { x }$ axis. 对合作绩效的反应是进入前学习时长\((\Lambda)\)的函数。代理平均具有乐观性，其估计值取自\(\beta(3,2)\)分布，精度取自\(\log_2 \beta(3,2)\)分布。\(\mathbf{x}\)轴采用对数刻度。

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