  In this paper, we study a large population game with heterogeneous dynamics
and cost functions solving a consensus problem. Moreover, the agents have
communication constraints which appear as: (1) an Additive-White Gaussian Noise
(AWGN) channel, and (2) asynchronous data transmission via a fixed scheduling
policy. Since the complexity of solving the game increases with the number of
agents, we use the Mean-Field Game paradigm to solve it. Under standard
assumptions on the information structure of the agents, we prove that the
control of the agent in the MFG setting is free of the dual effect. This allows
us to obtain an equilibrium control policy for the generic agent, which is a
function of only the local observation of the agent. Furthermore, the
equilibrium mean-field trajectory is shown to follow linear dynamics, hence
making it computable. We show that in the finite population game, the
equilibrium control policy prescribed by the MFG analysis constitutes an
$\epsilon$-Nash equilibrium, where $\epsilon$ tends to zero as the number of
agents goes to infinity. The paper is concluded with simulations demonstrating
the performance of the equilibrium control policy.
