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.
