Title: Zero-sum Stochastic Games with Asymmetric Information Show Chinese title

Title: 零和随机博弈中的信息不对称

Abstract: A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain conditions on the evolution of the common and private information, a dynamic programming characterization of the value of the game (if it exists) is presented. If the value of the zero-sum game does not exist, then the dynamic program provides bounds on the upper and lower values of the game. This dynamic program is then used for a class of zero-sum stochastic games with complete information on one side and partial information on the other, that is, games where one player has complete information about state, actions and observation history while the other player may only have partial information about the state and action history. For such games, it is shown that the value exists and can be characterized using the dynamic program. It is further shown that for this class of games, the dynamic program can be used to compute an equilibrium strategy for the more informed player in which the player selects its action using its private information and the common information belief. Show Chinese abstract

Abstract: 考虑了一个具有不对称信息的零和随机博弈的一般模型。在这个模型中，每个玩家在每个时间点的信息可以分为公共信息部分和私人信息部分。在对公共信息和私人信息演变的某些条件下，给出了博弈值（如果存在的话）的动态规划表征。如果零和博弈的值不存在，则动态规划提供了博弈上值和下值的界。然后，该动态规划被用于一类零和随机博弈，其中一方具有完全信息，另一方具有部分信息，即一方玩家对状态、动作和观测历史具有完全信息，而另一方玩家可能仅对状态和动作历史具有部分信息。对于这类博弈，证明了值的存在性，并可以使用动态规划进行表征。进一步证明，对于此类博弈，动态规划可用于计算更知情玩家的均衡策略，其中该玩家使用其私人信息和公共信息信念来选择其动作。