标题：A Semi-Tensor Product Approach to Finding Nash Equilibria for Static Games
作者：Guo Peilian; Wang Yuzhen; Li Haitao
作者机构：[Guo Peilian; Wang Yuzhen; Li Haitao] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China.
会议名称：32nd Chinese Control Conference (CCC)
会议日期：JUL 26-28, 2013
来源：2013 32ND CHINESE CONTROL CONFERENCE (CCC)
关键词：Static Game; Nash Equilibrium; Bayesian Nash Equilibrium; Pseudo-Boolean; Function; Semi-Tensor Product
摘要：This paper investigates how to find Nash equilibria (NE) for static games by using the semi-tensor product method, and presents a number of new results. First, the payoff function of each player for static games is expressed into an algebraic form via the semi-tensor product. Second, based on the algebraic form of the pseudo-Boolean derivative, two necessary and sufficient conditions are obtained for the existence of NE in the multi-player binary choice game with complete and incomplete information, respectively. Third, the multi-player multi-choice game is considered and two effective algorithms are established on how to find NE via the structural matrix of the payoff function. The study of illustrative examples shows that the new results/algorithms presented in this paper are very effective in finding NE for static games.