Efficient Decomposition of Bimatrix Games

TL;DR

This paper introduces a divide-and-conquer algorithm that leverages algebraic structures to efficiently compute Nash equilibria in bimatrix games, especially effective for games with small irreducible components.

Contribution

It presents a novel fixed-parameter tractable algorithm based on the algebraic decomposition of bimatrix games for faster equilibrium computation.

Findings

Significant performance improvements on small-parameter inputs

Algorithm effectively exploits algebraic structure

Demonstrates practical efficiency in bimatrix game analysis

Abstract

Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game as parameter. An implementation of the algorithm is shown to yield a significant performance increase on inputs with small parameters.