Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm
This work addresses the curse of dimensionality in analyzing finite-player network games for researchers in game theory and multi-agent systems, though it appears incremental as it builds on existing graphon game formulations.
The authors tackled the analysis and solution of stochastic games with heterogeneous agent interactions by proposing a discrete-time graphon game formulation using a representative player, proving existence and uniqueness of equilibrium under mild assumptions, and developing an online oracle-free learning algorithm with sample complexity analysis for convergence.
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.