Two Algorithms for Computing Exact and Approximate Nash Equilibria in Bimatrix Games

TL;DR

This paper introduces two algorithms for identifying strategic equivalence to zero-sum games and computing approximate Nash equilibria in bimatrix games, supported by extensive simulations.

Contribution

It presents novel algorithms for detecting strategic equivalence to zero-sum games and computing approximate Nash equilibria in bimatrix games.

Findings

Algorithms effectively identify strategic equivalence.

Algorithms successfully compute approximate Nash equilibria.

Numerical simulations demonstrate high efficacy of the methods.

Abstract

In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given bimatrix game is not strategically equivalent to a zero-sum game, we then propose an approach to compute a zero-sum game whose saddle-point equilibrium can be mapped to a well-supported approximate Nash equilibrium of the original game. We conduct extensive numerical simulation to establish the efficacy of the two algorithms.