The Value of Markov Chain Games with Lack of Information on One Side
The Value of Markov Chain Games with Lack of Information on One Side
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一方面缺乏信息的马尔可夫链博弈的价值
DOI：
10.1287/moor.1060.0199
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Jérôme Renault
中科院分区：
文献类型：
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作者：
Jérôme Renault
我们考虑一个两人零和博弈，由有限状态集上的马尔可夫链和由状态索引的矩阵博弈族给出。状态序列遵循马尔可夫链。在每个阶段开始时，只有玩家 1 知道当前状态，然后进行相应的矩阵游戏，并且在进入下一阶段之前，两个玩家都会观察所选择的动作。我们将这样的博弈称为一侧缺乏信息的马尔可夫链博弈。该模型概括了奥曼和马斯勒在一侧缺乏信息的零和重复博弈模型（对应于马尔可夫链的转移矩阵为单位矩阵的情况）。我们推广了Aumann和Maschler的证明，并从无限多阶段适当的非揭示辅助博弈的定义和研究出发，证明了一致值的存在性。与 Aumann 和 Maschler 模型的一个重要区别在于，这里玩家 1 使用信息和揭示相关信息的概念是不同的。
We consider a two-player zero-sum game, given by a Markov chain over a finite set of states and a family of matrix games indexed by states. The sequence of states follows the Markov chain. At the beginning of each stage, only Player 1 is informed of the current state, then the corresponding matrix game is played, and the actions chosen are observed by both players before proceeding to the next stage. We call such a game a Markov chain game with lack of information on one side. This model generalizes the model of Aumann and Maschler of zero-sum repeated games with lack of information on one side (which corresponds to the case where the transition matrix of the Markov chain is the identity matrix). We generalize the proof of Aumann and Maschler and, from the definition and the study of appropriate nonrevealing auxiliary games with infinitely many stages, show the existence of the uniform value. An important difference with Aumann and Maschler's model is that here the notions for Player 1 of using the information and revealing a relevant information are distinct.