A semi-tensor product approach to finding Nash equilibria for static games

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.