Article citationsMore>>

Nash, S.G. and Sofer, A. (1996) Linear and Nonlinear Programming. McGraw-Hill, New York.

has been cited by the following article:

• TITLE: Polynomial Time Method for Solving Nash Equilibria of Zero-Sum Games

  AUTHORS: Yoshihiro Tanaka, Mitsuru Togashi

  KEYWORDS: Zero-Sum Games, Nash Equilibria, Karmarkar’s Method, Polynomial Time

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.11 No.1, March 17, 2021

  ABSTRACT: There are a few studies that focus on solution methods for finding a Nash equilibrium of zero-sum games. We discuss the use of Karmarkar’s interior point method to solve the Nash equilibrium problems of a zero-sum game, and prove that it is theoretically a polynomial time algorithm. We implement the Karmarkar method, and a preliminary computational result shows that it performs well for zero-sum games. We also mention an affine scaling method that would help us compute Nash equilibria of general zero-sum games effectively.