Repeated games with incomplete information and discounting
分析了贴现重复博弈中不完全信息的情况,提出算法找出所有均衡收益,发现当玩家足够耐心时,贝叶斯纳什均衡收益可由有限次信息揭示的序贯均衡收益逼近,且均衡收益集通常大于无贴现或信念自由均衡的情况。
Abstract. We analyze discounted repeated games with incomplete information, such that the players' payoffs depend only on their own type (known-own payoff case). We describe an algorithm for finding all equilibrium payoffs in games for which there exists an open set of belief-free equilibria of Hörner and Lovo (2009). This includes generic games with one-sided incomplete information and a large and important class of games with multi-sided incomplete information. When players become sufficiently patient, all Bayesian Nash equilibrium payoffs can be approximated by payoffs in sequential equilibria in which information is revealed finitely many times. The set of equilibrium payoffs is typically larger than the set of equilibrium payoffs in repeated games without discounting, and larger than the set of payoffs obtained in belief-free equilibria. The results are illustrated in bargaining and oligopoly examples.