This award funds new research in the theory of repeated strategic interactions, also known as the theory of repeated games. This branch of game theory has proven to be enormously influential both in economics and other social sciences. Past research has been transformative in its effect on, in the way we think about cooperation among individuals in a society, repeated competition in markets, or international governance, among other important topics.
The current method for modeling this kind of repeated interaction applies best to situations in which participants in each period make simultaneous choices. However, in many real world situations of long-term interaction, participants take actions one at a time, such that the exact time of these actions exhibit some randomness. The investigator develops a new method for modeling such situations, aiming to obtain general theoretical insights and to applying the model in specific economic and social contexts. These applications range through many different topics, such as legislative bargaining, online auctions and oligopoly competition. The new methodological tools will offer ways to address research questions that are too difficult to answer using more standard models and pave the way for new research directions.
The award funds three distinct research projects. Project One: The research team investigates dynamic games in which players can only modify their actions at discrete random times, while they accumulate payoffs continuously according to the currently specified actions in a stage game. The researchers show that these games exhibit important differences relative to standard simultaneous move repeated games, both on finite and infinite time horizons. For example, with fixed finite horizon, there can be equilibria implying cooperation for most of the time horizon, even when the stage game has a unique noncooperative Nash equilibrium. The team provides an example of an infinite horizon game in which repetition of any of the static equilibria of the stage game is not an equilibrium of the dynamic game, and all stationary subgame perfect equilibria (sspe) involve nontrivial dynamics. The team has established the general existence of sspe (for any discount rate), and are characterizing of the limit set of all sspe payoffs as players become infinitely patient.
Project Two adapts the framework to investigates second-price online auctions like ebay, when bidders do not participate continuously at the auction, but instead receive random discrete opportunities to place or modify bids. The team shows that even when valuations are private and bidders can leave proxy bids, these games have many different equilibria on weakly undominated strategies, besides truthful bidding. These equilibria can involve gradual bidding, and waiting till the end of the auction to start placing bids. These results are consistent with the behavior we observe in a variety of online auctions.
Project Three continues the PI's previous work on continuous-time random recognition multilateral bargaining. The team is extending the analysis to bargaining over spatial policy outcomes, an important application of which is legislative bargaining when there cannot be monetary transfers among legislators. Their primary focus is identifying how the expected policy depends on the status quo outcome and the recognition probabilities of players, when the time horizon for negotiations is long. In another part of the project they are using the equal arrivals specification of their coalitional bargaining model to propose a noncooperatively founded cooperative solution concept.
Broader impacts include the use of these new methods by scholars across the social science disciplines, better understanding of the properties of online auctions, and the training of several graduate students in these new research methods.