%0 Journal Article
%T Nash Equilibrium of a Fixed-Sum Two-Player Game
%A Yoshihiro Tanaka
%J American Journal of Computational Mathematics
%P 346-357
%@ 2161-1211
%D 2024
%I Scientific Research Publishing
%R 10.4236/ajcm.2024.143017
%X It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.
%K Nash Equilibrium
%K Fixed-Sum Two-Player Game
%K Principal-Dual Interior Point Method
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=136229