This paper studies an $N$--agent cost-coupled game where the agents are connected via an unreliable capacity constrained network. Each agent receives state information over that network which loses packets with probability $p$. A Base station (BS) actively schedules agent communications over the network by minimizing a weighted Age of Information (WAoI) based cost function under a capacity limit $\mathcal{C} < N$ on the number of transmission attempts at each instant. Under a standard information structure, we show that the problem can be decoupled into a scheduling problem for the BS and a game problem for the $N$ agents. Since the scheduling problem is an NP hard combinatorics problem, we propose an approximately optimal solution which approaches the optimal solution as $N \rightarrow \infty$. In the process, we also provide some insights on the case without channel erasure. Next, to solve the large population game problem, we use the mean-field game framework to compute an approximate decentralized Nash equilibrium. Finally, we validate the theoretical results using a numerical example.

翻译：本文研究了一个$N$个智能体成本耦合博弈问题，其中智能体通过一个不可靠且容量受限的网络相互连接。每个智能体通过该网络接收状态信息，信息丢失概率为$p$。基站（BS）在容量限制$\mathcal{C} < N$下（每个时刻最多允许$\mathcal{C}$次传输尝试），通过最小化基于加权信息年龄（WAoI）的成本函数，主动调度网络中的智能体通信。在标准信息结构下，我们证明该问题可解耦为基站的调度子问题和$N$个智能体的博弈子问题。由于调度问题属于NP难组合优化问题，我们提出一种近似最优解，该解在$N \to \infty$时趋近最优解。在此过程中，我们还对无信道擦除情形提供了部分见解。随后，为求解大规模种群博弈子问题，我们采用平均场博弈框架计算近似分散纳什均衡。最后通过数值算例验证了理论结果。