  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.
