We introduce a class of networked Markov potential games where agents are
associated with nodes in a network. Each agent has its own local potential
function, and the reward of each agent depends only on the states and actions
of agents within a $\kappa$-hop neighborhood. In this context, we propose a
localized actor-critic algorithm. The algorithm is scalable since each agent
uses only local information and does not need access to the global state.
Further, the algorithm overcomes the curse of dimensionality through the use of
function approximation. Our main results provide finite-sample guarantees up to
a localization error and a function approximation error. Specifically, we
achieve an $\tilde{\mathcal{O}}(\epsilon^{-4})$ sample complexity measured by
the averaged Nash regret. This is the first finite-sample bound for multi-agent
competitive games that does not depend on the number of agents.

本研究提出了一种基于网络结构的马尔可夫潜在博弈模型，以及一种局部演员 - 评论家算法，利用函数逼近方法克服了维度诅咒，并给出了与局部误差和函数逼近误差有关的有限样本保证，实验证明该算法能够有效地处理多智能体竞争博弈问题。