An LP Approach for Solving Two-Player Zero-Sum Repeated Bayesian Games

作     者：Li, Lichun Langbort, Cedric Shamma, Jeff 

作者机构：FAMU FSU Coll Engn Tallahassee FL 32311 USA Univ Illinois Champaign IL 61801 USA King Abdullah Univ Sci & Technol Thuwal 23955 Saudi Arabia 

出 版 物：《IEEE TRANSACTIONS ON AUTOMATIC CONTROL》 (IEEE自动控制汇刊)

年 卷 期：2019年第64卷第9期

页      面：3716-3731页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 

基　　金：NSF AFOSR/MURI [FA9550-10-1-0573] 

主　　题：Bayesian game linear programming optimization 

摘      要：This paper studies two-player zero-sum repeated Bayesian games in which every player has a private type that is unknown to the other player, and the initial probability of the type of every player is publicly known. The types of players are independently chosen according to the initial probabilities, and are kept the same all through the game. At every stage, players simultaneously choose actions, and announce their actions publicly. For finite horizon cases, an explicit linear program is provided to compute players security strategies. Moreover, this paper shows that a player s sufficient statistics, which is independent of the strategy of the other player, consists of the belief over the player s own type, the regret over the other player s type, and the stage. Explicit linear programs, whose size is linear in the size of the game tree, are provided to compute the initial regrets, and the security strategies that only depends on the sufficient statistics. For discounted cases, following the same idea in the finite horizon, this paper shows that a player s sufficient statistics consists of the belief of the player s own type and the antidiscounted regret with respect to the other player s type. Besides, an approximated security strategy depending on the sufficient statistics is provided, and an explicit linear program to compute the approximated security strategy is given. This paper also obtains a bound on the performance difference between the approximated security strategy and the security strategy, and shows that the bound converges to 0 exponentially fast.