The relation between eigenvalue/eigenvector and matrix game

TL;DR

This paper explores the relationship between eigenvalues/eigenvectors and properties of matrix games, aiming to extend findings from special matrices to more general cases in game theory.

Contribution

It uncovers the connection between eigenvalues/eigenvectors and matrix game properties, which has been largely unexplored in existing literature.

Findings

Identifies specific relations for special matrices

Proposes extensions to general matrices

Provides theoretical insights into matrix game analysis

Abstract

Matrix game, which is also known as two person zero sum game, is a famous model in game theory. There are some well established theories about it, such as von Neumann minimax theorem. However, almost no literature have reported the relationship between eigenvalue/eigenvector and properties of matrix game. In this paper, we find such relation of some special matrices and try to extend some conclusions to general matrix.