Algorithms for Stochastic Games With Perfect Monitoring

• 成果类型: Article
• 署名作者: Abreu, Dilip; Brooks, Benjamin; Sannikov, Yuliy
• 署名单位: New York University; University of Chicago; Stanford University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA14357
• 发表日期: 2020
• 页码: 1661-1695
• 关键词: equilibria; DYNAMICS; RISK

摘要

We study the pure-strategy subgame-perfect Nash equilibria of stochastic games with perfect monitoring, geometric discounting, and public randomization. We develop novel algorithms for computing equilibrium payoffs, in which we combine policy iteration when incentive constraints are slack with value iteration when incentive constraints bind. We also provide software implementations of our algorithms. Preliminary simulations indicate that they are significantly more efficient than existing methods. The theoretical results that underlie the algorithms also imply bounds on the computational complexity of equilibrium payoffs when there are two players. When there are more than two players, we show by example that the number of extreme equilibrium payoffs may be countably infinite.