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

2025-12-21

AI Summary

Traditional equilibrium concepts in adversarial team games assume homogeneous utility functions across team members, yet neglecting utility heterogeneity can destabilize such equilibria. Method: This paper explicitly models inter-member utility differences and introduces the Co-opetition Equilibrium (CoE), a novel solution concept wherein team strategies are correlated to simultaneously enable internal cooperation and external competition; it further proposes Team-Maximizing CoE as an optimization variant. Contribution/Results: We rigorously prove the existence and stability of CoE, and demonstrate that equilibria under homogeneity assumptions may lack robustness. The framework establishes a new solution concept, provides theoretical foundations for heterogeneous team games, and opens avenues for algorithm design—bridging cooperative and competitive incentives within non-identical utility settings.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Humans and AI: Teamwork, Team formation
• Multiagent Systems: Adversarial Agents

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Addresses adversarial team games where players have differing utility functions.
• Proposes Co-opetition Equilibrium to stabilize outcomes in such games.
• Introduces team-maximizing CoE to optimize team utility in adversarial scenarios.

Innovation

• Introduces Co-opetition Equilibrium for adversarial team games
• Considers different utility functions among team players
• Proposes team-maximizing CoE to maximize team utility