Computing Equilibria of Dynamic Games

• 成果类型: Article
• 署名作者: Yeltekin, Sevin; Cai, Yongyang; Judd, Kenneth L.
• 署名单位: Carnegie Mellon University; University of Chicago; Stanford University; University System of Ohio; Ohio State University; National Bureau of Economic Research
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2016.1572
• 发表日期: 2017
• 页码: 337-356
• 关键词: subgame perfect equilibria; discounted repeated games; incomplete information; capacity; COMPETITION; INVESTMENT

摘要

We develop a numerical method for computing all pure strategy subgame-perfect equilibrium values of dynamic strategic games with discrete states and actions. We define a monotone mapping that eliminates dominated strategies, and when applied iteratively, delivers an accurate approximation to the true equilibrium payoffs of the underlying game. Our algorithm has three parts. The first provides an outer approximation to equilibrium values, constructed so that any value outside of this approximation is not an equilibrium value. The second provides an inner approximation; any value contained within this approximation is an equilibrium value. Together, the two approximations deliver a practical check of approximation accuracy. The third part of our algorithm delivers sample equilibrium paths. To illustrate our method, we apply it to a dynamic oligopoly competition with endogenous production capacity.