Hierarchical Decision-Making in Population Games

2025-09-06

AI Summary

Traditional population games fail to capture realistic multi-level decision-making structures. Method: This paper proposes a hierarchical game modeling framework wherein individuals delegate decision-making authority to agents representing their strategic interests, yielding a three-tier “individual–agent–population” architecture. We formulate a hierarchical game model with general convex constraints, enabling inter-agent strategic interactions and coupled constraints without requiring individuals to know global constraints. Leveraging equilibrium existence analysis and iterative algorithm convergence theory, we develop a systematic solution methodology. Contribution/Results: We establish, for the first time, the existence of generalized Nash equilibria under this hierarchical structure and prove the convergence of a distributed algorithm for computing them. Experimental validation on a capacity-constrained urban navigation application demonstrates both the expressive power and computational efficacy of the proposed framework.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

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
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper introduces a hierarchical framework for population games, where individuals delegate decision-making to proxies that act within their own strategic interests. This framework extends classical population games, where individuals are assumed to make decisions directly, to capture various real-world scenarios involving multiple decision layers. We establish equilibrium properties and provide convergence results for the proposed hierarchical structure. Additionally, based on these results, we develop a systematic approach to analyze population games with general convex constraints, without requiring individuals to have full knowledge of the constraints as in existing methods. We present a navigation application with capacity constraints as a case study.

Problem

• Extends classical population games with hierarchical decision-making delegation
• Analyzes population games with general convex constraints systematically
• Develops equilibrium and convergence results for multi-layer decision structures

Innovation

• Hierarchical framework with delegated proxy decision-making
• Analyzes games with convex constraints sans full knowledge
• Establishes equilibrium properties and convergence results