Beliefs and Private Monitoring

这个研究项目涉及与私人监控的重复博弈相关的项目：博弈中的策略取决于私人观察到的变量。这类游戏允许对现实生活中重要的经济互动（如卡特尔、伙伴关系和雇主-雇员关系）进行严格的建模。虽然是现实的，但私人监督的假设已被证明是繁琐的，这在很大程度上是由于难以核实简单战略是否为均衡。因此，许多先前的研究提出了有效但不太可能在现实中观察到的奇异均衡，但可以检查激励条件以验证它们确实是均衡。这个项目的第一部分发展并提出了基于集合的方法来构造这类博弈的均衡。注意力被限制在一大类现实的策略——那些可以被表示为有限自动机的策略。它带来了一种可靠的方法，用于验证任何特定策略是否是均衡。这种核查以前被认为是一项困难的，甚至是不可能的任务。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平衡。该项目的第二部分需要开发基于网络的计算机代码，使用户可以轻松地将开发的方法应用于自己的经济应用。第三部分运用新发展的方法研究策略类的鲁棒性。如果一种策略不仅适用于所讨论的游戏，而且适用于具有轻微扰动收益的邻近游戏，那么它就被认为是稳健均衡。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，如果假设的动态策略在收益的小不确定性中存活下来，那么这种鲁棒性检查的概念就会出现。在这里，初步结果是简单而明确的：当且仅当平衡仅是最后k个游戏周期的函数（对于某些有限的k）时，平衡是稳健的。更广泛的影响：正式研究现实复杂的重复人类互动的能力，这些互动必然涉及一些人看到并采取行动，与其互动的其他人（例如竞争对手、合作伙伴、负责人、同事等）看不到的信号和行动。

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.