Information structures and values in zero-sum stochastic games
Information structures and values in zero-sum stochastic games
复制标题
零和随机博弈中的信息结构和价值
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Abhishek K. Gupta
中科院分区：
文献类型：
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作者：
A. Nayyar;Abhishek K. Gupta
我们考虑一个零和随机博弈，其中两个参与者对全局状态有一个共同的观察，每个参与者在每个时间步对其局部状态进行一个私人观察。参与者之间的信息不对称使得很难计算均衡成本（称为零和游戏的价值）。为了帮助我们确定这样一个博弈的价值，我们首先考虑一个只有公共观察而没有局部状态的博弈。我们认为，这个游戏的价值与对称信息可以计算使用信息结构的扩展，然后在[1]中描述的方法。然后，我们认为，具有全局和局部状态的非对称信息博弈的价值等于具有对称信息的虚拟博弈的价值。这使我们能够使用对称信息博弈的结果来计算具有全局和局部状态的博弈的值。
We consider a zero-sum stochastic game where two players have a common observation of a global state, and each player makes a private observation of its local state at every time step. This asymmetry of information among the players makes it difficult to the compute the equilibrium cost (called the value of the zero-sum game). To help us determine the value of such a game, we first consider a game with just the common observations and no local state. We argue that the value of this game with symmetric information can be computed using an information structure expansion followed by the methodology described in [1]. We then argue that the value of the asymmetric information game with global and local states is equal to the value of a virtual game with symmetric information. This allows us to use the results for the symmetric information game for computing the value of the game with global and local states.