Dynamical Analysis of a Repeated Game with Incomplete Information
研究雷诺提出的两人重复零和博弈，其中状态遵循马尔可夫演化，将已知最优策略的适用范围从[公式]扩展到约[公式]，并证明其在0.7328附近失效，使用了动力学系统中的压力概念。
We study a two player repeated zero-sum game with asymmetric information introduced by Renault in which the underlying state of the game undergoes Markov evolution (parameterized by a transition probability, p, in the range [Formula: see text] to 1). Hörner, Rosenberg, Solan and Vieille identified an optimal strategy, σ * for the informed player for p in the range [Formula: see text]. We extend the range on which σ * is proved to be optimal to about [Formula: see text] and prove that it fails to be optimal at a value around 0.7328. Our techniques make use of tools from dynamical systems, specifically the notion of pressure, introduced by D. Ruelle.