Nonparametric Identification and Estimation of Bargaining Models

讨价还价理论在过去的三十年里蓬勃发展。原先的两个参与者交替提出报价和还价的讨价还价模型已经在多个方向上得到扩展，允许更一般的谈判协议和两个以上的参与者。理论文献的发展与议价模型的广泛应用密切相关，并且在很大程度上是由议价模型的广泛应用推动的。这些谈判包括劳动、家庭、法律、住房、政治、国际和医疗谈判。关于此类谈判结果以及讨价还价过程细节的数据的可用性增加，也刺激了实证工作的激增，其中偶然的经验主义逐渐导致更系统地尝试将战略讨价还价模型应用于数据。在理论和实证应用中得到广泛研究的两个议价框架是随机顺序议价模型和非常见先验议价。在随机顺序议价模型中，剩余分配（或“蛋糕”）和议价协议（游戏邦注：即玩家提出条件和还价的顺序）可以根据随机过程随时间演变。这个特性使模型更加灵活（它为大量的议价博弈提供了一个统一的框架）。它还使拖延达成协议的现象合理化，这种情况在实际谈判中经常出现。随机谈判框架已被用于各种实证应用，从议会民主联合政府的组建，到集体谈判协议，到公司破产重组，到产品市场行业标准的制定，以及主权债务的重新谈判。具有不寻常优先权的讨价还价模型也合理化了达成协议时出现的延迟，并且代表了理论和应用研究的一个快速增长的领域。在这些模型中，参与者对未能达成协议的后果有不同的期望，这在几个谈判情境中是合理的。例如，具有不寻常优先权的议价模型已被用于研究医疗事故诉讼中的争议解决过程或公司签署广泛交叉许可协议的动机，以及半导体行业广泛交叉许可谈判的持续时间。尽管讨价还价模型在经济应用中的重要性，但对于这些模型的结构要素或反事实环境中的讨价还价结果是否可以在不施加参数假设的情况下被识别和估计，人们知之甚少。本文提出的研究将对议价模型的估计文献做出贡献，在参与者风险厌恶和具有异质折扣因素的随机议价模型和参与者具有不寻常先验的议价模型的非参数识别和估计中提供积极的结果。本研究的统一主题是，这两类模型都可以解释达成协议延迟的发生，并且具有经验相关性，因为在许多应用中，风险规避、时间偏好贴现率的异质性和过度乐观可能在确定谈判协议的时间和条款方面发挥重要作用。

Bargaining theory has flourished in the past thirty years. The original model of bargaining between two players who alternate in making offers and counteroffers has been extended in a number of directions allowing for more general negotiation protocols and more than two players. The development of the theoretical literature has gone hand in hand with, and for a large part has been motivated by, the broad range of applications of bargaining models. These include labor, family, legal, housing, political, international and medical negotiations. The increased availability of data on the outcomes of such negotiations, as well as on the details of the bargaining process, has also stimulated a surge in empirical work, where casual empiricism has progressively led the way to more systematic attempts to take strategic bargaining models to data.Two bargaining frameworks that have been extensively studied in theoretical and empirical applications are the stochastic sequential bargaining model, and bargaining with uncommon priors. In the model of stochastic sequential bargaining, the surplus to be allocated (or the "cake") and the bargaining protocol (i.e. the order in which players can make offers and counteroffers), are allowed to evolve over time according to a stochastic process. This feature makes the model flexible (it provides a unified framework for a large class of bargaining games). It also rationalizes the occurrence of delays in reaching an agreement, which are often observed in actual negotiations. The stochastic bargaining framework has been used in a variety of empirical applications that range from the formation of coalition governments in parliamentary democracy, to collective bargaining agreements, to corporate bankruptcy reorganizations, to the setting of industry standards in product markets, and to sovereign debt renegotiations.Models of bargaining with uncommon priors also rationalize the occurrence of delays in reaching an agreement, and represent a fast-growing area of both theoretical and applied research. In these models, players have different expectations regarding the consequences of failing to reach an agreement, which is a plausible scenario in several bargaining situations. For example, bargaining models with uncommon priors have been used to study the process of dispute resolution in medical malpractice litigation or the incentives of firms to sign broad cross-license agreements as well as the duration of broad cross-license negotiations in the semiconductor industry.In spite of the importance of bargaining models in economic applications, little is known about whether the structural elements of these models or the bargaining outcomes in counterfactual environments can be identified and estimated without imposing parametric assumptions. The proposed research will contribute to the literature on the estimation of bargaining models by providing positive results in the nonparametric identification and estimation of stochastic bargaining models where players are risk-averse and have heterogeneous discount factors, and of bargaining models where players have uncommon priors. The unifying theme of this research is that both classes of models may explain the occurrence of delays in reaching an agreement and are relevant empirically, as in many applications risk aversion, heterogeneity in the discount rate of time preference, and excessive optimism are likely to play an important role in determining the timing and terms of negotiation agreements.