Characterization of Potential Games: Application in Aggregative Games

TL;DR

This paper characterizes potential games within the class of aggregative games, providing simplified criteria and methods to identify potential games, and demonstrates the approach using Cournot game examples.

Contribution

It introduces a payoff-based method to identify potential games and simplifies the conditions for aggregative games to be classified as potential games.

Findings

The method successfully identifies potential games in Cournot examples.

Simplified criteria effectively classify aggregative games as potential games.

Potential functions are explicitly derived for tested game instances.

Abstract

The main objective of this work is to describe games which fall under title of Potential and simplify the conditions for class of aggregative games. Games classified as aggregative are ones in which, in addition to the player's own action, the payoff for each player depends on an aggregate of all the players' decision variables. In this study, we developed a method based on payoff functions to determine if a given game is potential. Then, in order to identify the Aggregative Games that fall under this class we simplified the criteria for the class of Aggregative Games. A $3$-player Cournot game, also known as an Aggregative Potential Game, is used to test the characterization criteria for Potential Games. A $4$-player Cournot game is also utilized to test the form of potential function we obtained for class of general potential games.