Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm

TL;DR

This paper introduces a graphon mean field game framework with a representative player for analyzing stochastic games with heterogeneous interactions, providing theoretical guarantees and a learning algorithm for equilibrium computation.

Contribution

It develops a novel graphon game formulation with a representative player, proves equilibrium existence and uniqueness, and presents an oracle-free learning algorithm with convergence analysis.

Findings

Proved existence and uniqueness of the graphon equilibrium.

Constructed approximate solutions for finite network games.

Developed an online learning algorithm with sample complexity guarantees.

Abstract

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.