Generalized Nash Equilibrium Solutions in Dynamic Games With Shared Constraints

2025-02-26

AI Summary

This paper addresses the computation of generalized Nash equilibria (GNEs) in dynamic games with shared constraints. Conventional normalized formulations impose a common Lagrange multiplier across all players, thereby excluding numerous non-normalized GNEs. To overcome this limitation, we propose the first modeling framework based on mixed complementarity problems (MCPs) for systematically computing non-normalized GNEs. Building upon variational inequality theory and numerical optimization, we further develop an optimal GNE selection mechanism that enables decision-makers to choose equilibria according to predefined criteria—such as fairness, efficiency, or robustness. Numerical experiments demonstrate that the proposed approach successfully identifies diverse non-normalized equilibria missed by traditional methods, significantly enhancing both the practicality of the solution set and the flexibility of strategic decision-making.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used, this approach excludes other potentially valuable GNE. This paper presents a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized GNE, expanding the solution space. We also propose a systematic approach for selecting the optimal GNE based on predefined criteria, enhancing practical flexibility. Numerical examples illustrate the methods effectiveness, offering an alternative to traditional normalized solutions.

Problem

• Computes non-normalized GNE in dynamic games
• Expands solution space beyond normalized GNE
• Selects optimal GNE based on predefined criteria

Innovation

• MCP formulation for GNE
• Non-normalized solution expansion
• Optimal GNE selection criteria