On Potential Equations of Finite Games

TL;DR

This paper introduces new criteria and minimal verification equations for identifying potential finite games, establishing connections with existing characterizations and showing that a game is potential if all its bi-matrix sub-games are potential.

Contribution

It proposes novel criteria and minimal verification equations for potential games, linking potential equations with existing characterizations and demonstrating the potentiality of a game through its sub-games.

Findings

New criteria for potential game detection

Minimal verification equations introduced

Potentiality of a game linked to its sub-games

Abstract

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time. Some connections between the potential equations and the existing characterizations of potential games are established. It is revealed that a finite game is potential if and only if its every bi-matrix sub-game is potential.