Nonparametric Identification and Estimation of Bargaining Models

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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.