Hierarchical Decision-Making in Population Games

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.