When Does Selfishness Align with Team Goals? A Structural Analysis of Equilibrium and Optimality

2025-08-18

AI Summary

This work addresses performance degradation in non-cooperative teams arising from selfish individual decisions. We propose a parametric game model to characterize the misalignment between individual and team objectives, derive necessary and sufficient conditions for Nash equilibrium to coincide with the team-optimal solution, and establish an upper bound on the resulting performance gap. Innovatively, we integrate hypergradient-based optimization into a non-convex, non-smooth bilevel framework to design tunable individual objective parameters that steer the Nash equilibrium toward the team optimum. We provide theoretical convergence guarantees—showing that the algorithm converges to a critical point—and validate the tightness of the derived performance bound and the feasibility of parameter tuning via numerical simulations. To our knowledge, this is the first work to enable interpretable modeling and controllable optimization of systemic performance degradation in non-cooperative multi-agent systems.

Technology Category

• Multiagent Systems: Teamwork
• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This paper investigates the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of self-interested decisions on team performance. In classical team decision problems, team members typically act cooperatively towards a common objective to achieve a team-optimal solution. However, in practice, members may behave selfishly by prioritizing their goals, resulting in an NE under a non-cooperative game. To study this misalignment, we develop a parameterized model for team and game problems, where game parameters represent each individual's deviation from the team objective. The study begins by exploring the consistency and deviation between the NE and the team-optimal solution under fixed game parameters. We provide a necessary and sufficient condition for any NE to be a team optimum, along with establishing an upper bound to measure their difference when the consistency condition fails. The exploration then focuses on aligning NE strategies towards the team-optimal solution through the adjustment of game parameters, resulting in a non-convex and non-smooth bi-level optimization problem. We propose a hypergradient-based algorithm for this problem, and establish its convergence to the critical points. Finally, we validate our theoretical findings through extensive simulation studies.

Problem

• Analyzing alignment between Nash equilibrium and team-optimal solutions
• Measuring impact of selfish behavior on team performance outcomes
• Developing optimization method to align individual and team goals

Innovation

• Parameterized model for team-game deviation analysis
• Hypergradient-based algorithm for bi-level optimization
• Necessary and sufficient condition for equilibrium optimality