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.

翻译：我们提出了一种基于代表参与者的连续状态与动作空间上的离散时间图论博弈框架，用于研究具有异质性交互的多智能体随机博弈。相较于广泛采用的连续玩家数框架，该公式在哲学和数学上均具有优势。我们在温和假设下证明了图论均衡的存在唯一性，并表明该均衡可用于构造网络有限玩家博弈的近似解——此类博弈因维度灾难而难以分析与求解。进一步地，我们开发了一种无需在线预言机的学习算法以数值求解该均衡，并给出了其收敛性的样本复杂度分析。