On Matrix Method of Symmetric Games

TL;DR

This paper introduces an improved matrix semi-tensor product method based on adjacent transpositions for analyzing symmetric games, simplifying the process of testing and characterizing such games with new conditions and bases.

Contribution

The paper presents a novel version of the matrix semi-tensor product method utilizing adjacent transpositions, enhancing the analysis of symmetric games.

Findings

Simplified testing of symmetric games using the new method

Derived new necessary and sufficient conditions for symmetric games

Provided concrete examples demonstrating effectiveness

Abstract

This paper provides a new version of matrix semi-tensor product method based on adjacent transpositions to test symmetric games. The advantage of using adjacent transpositions lies in the great simplification of analysis of symmetric games. By using the new method, new necessary and sufficient conditions for symmetric games are proposed, and a group of bases of a symmetric game space can be easily calculated. Moreover, the testing equations with the minimum number can be concretely determined. Finally, two examples are displayed to show the effectiveness of the proposed method.