Project 1: (Infinitely) repeated games have widespread application in economics as simple and tractable models of ongoing strategic relationships between agents. Despite an extensive literature on repeated games, the case where agents privately monitor the behavior of their opponents has been known for its intractability. This case is important as real-life relationships, where monitoring is not private, are even hard to imagine. It is now a famous open question whether the folk theorem extends to the case of private monitoring.
This project intends to address this open question. A recent working paper of Ely, Hoerner, and Olszewski studies a class of strategies that generalizes examples constructed in the literature for the Prisoners Dilemma. The Prisoners Dilemma strategies were more tractable than others. The paper provides a simple and sharp characterization of equilibrium payoffs that can be achieved by using those strategies. While those strategies can support a large set of payoffs, they are not rich enough to generate a folk theorem.
The research strategy in a follow-up study by Hoerner and Olszewski relies on progressive enlarging of the class of strategies, sacrificing as little tractability as possible but generating more equilibrium payoffs. It is believed that this strategy should lead at least to the folk theorem for all two-player games with almost-perfect monitoring.
Project 2: This project has been inspired by the potential of sets of lotteries as a modeling tool. Sets of lotteries have recently been used to model the preference for flexibility as well as self-control problems, such as temptation-driven preferences. A recent working paper of Olszewski uses them to provide an alternative model for studying ambiguity. Traditionally, ambiguity has been studied within the Savage setting, which instead of sets of lotteries considers mappings from a state space into the outcomes. Both ambiguity and temptation-driven preferences apply to a wide range of economically important situations, and there seem to be a demand for better tools to analyzing these phenomena.
It is believed that a model that considers correspondences from a state space into sets of lotteries would be not only an joint tool for studying several phenomena, but it would also respond to several possible criticisms of the existing models of the preference for flexibility and self-control problems.
Private monitoring in ongoing relationships, ambiguous information, and self-control problems are widely present in the surrounding us world. It is - referring to most standard examples - commonly believed that the studies on ambiguity contribute to the understanding of financial markets, in particular equity premium puzzle, and that the studies on private monitoring in repeated games have implications on collusive behavior in oligopoly markets and antitrust regulations. These projects will develop techniques for thinking about private monitoring within equilibrium setting, as well as it will improve tools for studying ambiguous information, and self-control problems. Private monitoring attracts attention from sociologists and anthropologists, while ambiguity and self-control problems are subjects of active research by psychologists.
