Algorithms for Stochastic Games With Perfect Monitoring. Issue 4 (23rd July 2020)

• Record Type: Journal Article
• Authors: Abreu, Dilip; Brooks, Benjamin; Sannikov, Yuliy
• Is Part Of: Econometrica. Volume 88:Issue 4(2020)
• Page Start: 1661
• Page End: 1695
• Publication Date: 2020-07-23
• Subjects: Stochastic game -- perfect monitoring -- algorithm -- computation; Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA14357
• Languages: English
• ISSNs: 0012-9682

Abstract

Abstract : 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.