Beliefs and Private Monitoring

这项研究计划涉及与私人监控的重复游戏有关的项目：游戏中的策略依赖于私人观察的变量。这类游戏允许对重要的现实生活中的经济互动进行严格的建模，例如卡特尔、合作伙伴关系和雇主-雇员关系。尽管现实，但事实证明，私人监督的假设很麻烦，这在很大程度上是因为很难核实简单的战略是否是均衡的。鉴于此，许多先前的研究提出了有效但奇异的均衡，在现实中不太可能观察到，但激励条件可以被检查以验证它们确实是均衡。本项目的第一部分发展并提出了基于集合的方法来构建这类博弈的均衡。人们的注意力仅限于一大类现实的策略--那些可以用有限自动机表示的策略。它导致了一种可靠的方法来验证任何特定的策略是否是均衡。此前，这种核查被描述为一项困难的任务，如果不是不可能的话。使用这些方法，可以在笔记本电脑上在几分之一秒内验证简单的均衡。该项目的第二部分需要开发基于网络的计算机代码，使用户能够很容易地将所开发的方法应用于他们自己的经济应用。第三部分利用新发展的方法研究了策略类的稳健性。一种策略被认为是稳健均衡，如果它不仅是有问题的博弈的均衡，而且是收益略有扰动的邻近博弈的均衡。在现实生活中，玩家不太可能对彼此的收益有共同的了解，因此，如果假设的动态策略在收益的微小不确定性中幸存下来，这种稳健性的概念就会得到检验。在这里，初步的结果是简单而严酷的：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：能够正式研究现实中复杂的重复的人类互动，这必然涉及一些人看到其他人(例如，竞争对手、合作伙伴、校长、同事等)的信号和行动并采取行动。他们与之互动的人看不到。

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.