Common Information Based Markov Perfect Equilibria for Stochastic Games With Asymmetric Information: Finite Games
Common Information Based Markov Perfect Equilibria for Stochastic Games With Asymmetric Information: Finite Games
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DOI：
10.1109/tac.2013.2283743
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发表时间：
2014-03
影响因子：
6.8
通讯作者：
A. Nayyar;Abhishek K. Gupta;Cédric Langbort;T. Başar
中科院分区：
文献类型：
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作者：
A. Nayyar;Abhishek K. Gupta;Cédric Langbort;T. Başar
随机博弈模型，其中多个控制器共同控制的动态系统的状态的演变，但有机会获得不同的信息的状态和动作过程被认为是。控制器之间的信息不对称使得难以计算或表征纳什均衡。利用控制者之间的共同信息，利用非对称信息博弈构造另一个对称信息博弈，使得新博弈的均衡可以转化为原博弈的均衡.在一定条件下，证明了新的对称信息博弈的马尔可夫状态，并刻画了其马尔可夫完美均衡。这一特征提供了一个逆向归纳算法，以找到纳什均衡的原始游戏与不对称信息的纯策略或行为。该算法的每一步都涉及到寻找一个单阶段贝叶斯博弈的贝叶斯纳什均衡。原始博弈的纳什均衡类，可以在这种落后的方式被称为共同信息为基础的马尔可夫完美均衡。
A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information among the controllers makes it difficult to compute or characterize Nash equilibria. Using the common information among the controllers, the game with asymmetric information is used to construct another game with symmetric information such that the equilibria of the new game can be transformed to equilibria of the original game. Further, under certain conditions, a Markov state is identified for the new symmetric information game and its Markov perfect equilibria are characterized. This characterization provides a backward induction algorithm to find Nash equilibria of the original game with asymmetric information in pure or behavioral strategies. Each step of this algorithm involves finding Bayesian Nash equilibria of a one-stage Bayesian game. The class of Nash equilibria of the original game that can be characterized in this backward manner are named common information based Markov perfect equilibria.