Beliefs and Private Monitoring

该研究计划涉及与私人监控的重复游戏相关的项目：策略依赖于私人观察变量的游戏。 这样的游戏允许对现实生活中重要的经济互动进行严格的建模，如卡特尔，合作伙伴关系和雇主-雇员关系。 虽然现实，私人监督的假设已被证明是繁琐的，在很大程度上是由于难以验证简单的策略是否是均衡。 由于这一点，许多以前的研究已经提出了有效的，但异国情调的均衡不太可能在现实中观察到，但激励条件可以检查，以验证他们确实是equilibria. First部分这个项目的发展，并提出了基于集合的方法来构建这类游戏的均衡。 注意力被限制在一大类现实的战略-那些可以表示为有限自动机。 它导致了一个强大的方法来验证任何特定的策略是否是一个均衡。 这种核查以前曾被描述为一项即使不是不可能，也是困难的任务。 使用这些方法，简单的平衡可以在几分之一秒内在笔记本电脑上验证。 该项目的第二部分需要开发基于网络的计算机代码，使用户能够轻松地将开发的方法应用于自己的经济应用。第三部分利用新发展的方法研究了各类策略的鲁棒性。 一个策略被认为是稳健均衡，如果它不仅是所讨论的博弈的均衡，而且是具有轻微扰动收益的邻近博弈的均衡。 现实生活中的参与者不太可能对彼此的收益有共同的了解，因此这种鲁棒性的概念检查假设的动态策略是否能在收益的小不确定性中生存下来。 在这里，初步的结果是简单而鲜明的：一个均衡是稳健的当且仅当它是最后k个博弈周期的函数（对于某个有限的k）。 更广泛的影响：能够正式研究现实复杂的重复人类互动，这必然涉及一些人看到，并采取行动，其他人（例如，竞争对手，合作伙伴，负责人，同事等）的信号和行动。与他们互动的人看不见。

This research program entails projects related to repeated games with private monitoring: games in which strategies depend on privately observed variables. Such games allow the rigorous modeling of important real-life economic interactions such as cartels, partnerships, and employer-employee relationships. While realistic, the assumption of private monitoring has proved cumbersome, in large part due to the difficulty in verifying whether simple strategies are, or are not, equilibria. Due to this, many previous studies have proposed valid but exotic equilibria unlikely to be observed in reality but where incentives conditions can be checked to verify that they are indeed equilibria.The first part of this project develops and presents set-based methods for constructing equilibria in this class of games. Attention is restricted to a large class of realistic strategies - those which can be represented as finite automata. It leads to a robust methodology for verifying whether any particular strategy is, or is not, an equilibrium. Such verification had previously been described as a difficult, if not impossible, task. Using these methods, simple equilibria can be verified on a laptop computer in a fraction of a second. The second part of this project entails the development of web-based computer codes to allow the users to easily apply the developed methods for their own economic applications. The third part uses the newly developed methods to study the robustness of classes of strategies. A strategy is considered a robust equilibrium if it is an equilibrium not only for the game in question, but an equilibrium for near-by games with slightly perturbed payoffs. Players in real-life situations are unlikely to have common knowledge of each others' payoffs and hence this notion of robustness checks if postulated dynamic strategies survive small uncertainty about payoffs. Here, preliminary results are simple and stark: an equilibrium is robust if and only if it is a function only of the last k periods of play (for some finite k). Broader Impacts: The ability to formally study realistically complex repeated human interactions which necessarily involve some people seeing, and acting upon, signals and actions that other people (for example, competitors, partners, principals, co-workers etc.) with whom they interact do not see.