Deviation Between Team-Optimal Solution and Nash Equilibrium in Flow Assignment Problems

2025-03-31

AI Summary

This paper investigates the strategic deviation between the team-optimal solution and Nash equilibria in traffic assignment problems, quantifying the degradation of system-wide performance due to individual selfishness. Methodologically, it integrates game theory, optimization theory, and potential game analysis to systematically characterize upper bounds on this deviation under both unique and multiple equilibrium regimes. It establishes a necessary and sufficient condition: the team-optimal solution coincides with all Nash equilibria if and only if the game is a potential game—thereby eliminating the strategic trade-off dilemma. Numerical simulations validate the tightness of the derived deviation bounds and the robustness of the consistency condition. The core contributions are threefold: (i) a formal framework for quantifying strategic deviation, (ii) closed-form analytical expressions for deviation upper bounds, and (iii) the identification of the precise condition under which Nash equilibria and the team optimum are aligned.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate the relationship between the team-optimal solution and the Nash equilibrium (NE) to assess the impact of strategy deviation on team performance. As a working use case, we focus on a class of flow assignment problems in which each source node acts as a cooperating decision maker (DM) within a team that minimizes the team cost based on the team-optimal strategy. In practice, some selfish DMs may prioritize their own marginal cost and deviate from NE strategies, thus potentially degrading the overall performance. To quantify this deviation, we explore the deviation bound between the team-optimal solution and the NE in two specific scenarios: (i) when the team-optimal solution is unique and (ii) when multiple solutions do exist. This helps DMs analyze the factors influencing the deviation and adopting the NE strategy within a tolerable range. Furthermore, in the special case of a potential game model, we establish the consistency between the team-optimal solution and the NE. Once the consistency condition is satisfied, the strategy deviation does not alter the total cost, and DMs do not face a strategic trade-off. Finally, we validate our theoretical analysis through some simulation studies.

Problem

• Study deviation between team-optimal solution and Nash equilibrium in flow assignment
• Analyze impact of selfish decision makers on team performance degradation
• Establish consistency conditions to eliminate strategic trade-offs in potential games

Innovation

• Analyze deviation between team-optimal and Nash equilibrium
• Establish consistency in potential game models
• Validate theory via simulation studies