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https://doi.org/10.1016/0024-3795(91)90275-2

has been cited by the following article:

• TITLE: Nash Equilibrium of a Fixed-Sum Two-Player Game

  AUTHORS: Yoshihiro Tanaka

  KEYWORDS: Nash Equilibrium, Fixed-Sum Two-Player Game, Principal-Dual Interior Point Method

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.14 No.3, September 25, 2024

  ABSTRACT: 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.