Econometric models of strategic interactions among people or firms have received a great deal of attention in the literature. Less attention has been paid to the role of the underlying assumptions about the way agents form beliefs about other agents. We focus on a single large Bayesian game with idiosyncratic strategic neighborhoods and develop an approach of empirical modeling that relaxes the assumption of rational expectations and allows the players to form beliefs differently. By drawing on the main intuition of Kalai (2004), we introduce the notion of hindsight regret, which measures each player's ex-post value of other players' type information, and obtain the belief-free bound for the hindsight regret. Using this bound, we derive testable implications and develop a bootstrap inference procedure for the structural parameters. Our inference method is uniformly valid regardless of the size of strategic neighborhoods and tends to exhibit high power when the neighborhoods are large. We demonstrate the finite sample performance of the method through Monte Carlo simulations.

翻译：有关个人或企业之间战略互动的计量经济学模型在文献中备受关注，但关于行为者如何形成对其他行为者信念的潜在假设所起的作用却较少受到重视。我们聚焦于一个具有异质性战略邻域的单一大规模贝叶斯博弈，并发展了一种经验建模方法，该方法放宽了理性预期假设，允许参与者以不同方式形成信念。借鉴Kalai（2004）的主要直觉，我们引入了事后遗憾这一概念，用以衡量每位参与者在事后对其他参与者类型信息的价值，并获得了事后遗憾的无信念界限。利用这一界限，我们推导出可检验的推断，并开发了一种用于结构参数的自举推断程序。无论战略邻域的规模如何，我们的推断方法均具有一致有效性，且在邻域较大时往往表现出较高的检验功效。我们通过蒙特卡洛模拟展示了该方法的有限样本性能。