Considering the Difference in Utility Functions of Team Players in Adversarial Team Games

TL;DR

This paper introduces a new equilibrium concept for adversarial team games that accounts for differing utility functions among team players, improving stability and strategic cooperation in AI models of adversarial scenarios.

Contribution

It proposes the Co-opetition Equilibrium (CoE), a novel solution concept that models cooperation among team players with different utilities against an adversary.

Findings

Ignoring utility differences causes unstable equilibria.

CoE improves stability by modeling cooperation among diverse team players.

Team-maximizing CoE enhances team utility in adversarial settings.

Abstract

The United Nations' 2030 Agenda for Sustainable Development requires that all countries collaborate to fight adversarial factors to achieve peace and prosperity for humans and the planet. This scenario can be formulated as an adversarial team game in AI literature, where a team of players play against an adversary. However, previous solution concepts for this game assume that team players have the same utility functions, which cannot cover the real-world case that countries do not always have the same utility function. This paper argues that studying adversarial team games should not ignore the difference in utility functions of team players. We show that ignoring the difference in utility functions of team players could cause the computed equilibrium to be unstable. To show the benefit of considering the difference in utility functions of team players, we introduce a novel solution concept called Co-opetition Equilibrium (CoE) for the adversarial team game. In this game, team players with different utility functions (i.e., cooperation between team players) correlate their actions to play against the adversary (i.e., competition between the team and the adversary). We further introduce the team-maximizing CoE, which is a CoE but maximizes the team's utility among all CoEs. Both equilibria can overcome the issue caused by ignoring the difference in utility functions of team players. We further show the opportunities for theoretical and algorithmic contributions based on our position of considering the difference in utility functions of team players.