Collaborative Research: New Algorithms for Computing Equilibria of Stochastic Games

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This research focuses on models of dynamic strategic behavior, in which two parties (individuals, nations, corporations, agencies) interact repeatedly over a long horizon and make decisions that have a persistent impact on the environment. The PIs are developing algorithms to simulate behavior in which each party has consistent beliefs about how others will behave and is maximizing their own welfare given those beliefs. These computational methods can be applied to a wide range of models that are used in various fields of economics, as well as in other disciplines such as international relations and evolutionary biology.More specifically, the PIs study the pure strategy subgame perfect equilibria of infinitely repeated games with geometric discounting and a stochastic state variable. The state variable determines the set of actions that can be taken by the agents in each period of the game and the resultant payoffs. Conditional on the actions taken by the players, the state evolves as a Markov chain. The objective of the research is to develop algorithms for computing the discounted payoffs that players can obtain in subgame perfect equilibria starting in each state. The PIs will also develop and distribute software packages that implement the algorithms.