Large Population Games with Timely Scheduling over Constrained Networks

In this paper, we consider a discrete-time multiagent system involving N cost-coupled networked rational agents solving a consensus problem, and a central Base Station (BS), scheduling agent communications over a network. Due to an average bandwidth constraint on the number of transmissions, the BS can let at most Rd < N agents to access their state information through the network on average. For the scheduling problem, we propose a novel weighted age of information (WAoI) metric. Then, under standard information structures, we are able to separate the estimation and control problems for each agent. We first solve an unconstrained MDP problem and then compute an optimal policy for the original problem using the solution to the former problem. Next, we solve the consensus problem using the mean-field game framework wherein we first design decentralized control policies for a limiting case of the N-agent system as N → ∞, and prove the existence of a unique mean-field equilibrium. Consequently, we show that the obtained equilibrium policies constitute an ϵ-Nash equilibrium for the finite agent system. Finally, we validate the performance of both the scheduling and the control policies through numerical simulations.