Coordination in Distributed Networks via Coded Actions With Application to Power Control

This paper investigates the problem of coordinating several agents through their actions, focusing on an asymmetric observation structure with two agents. Specifically, one agent knows the past, present, and future realizations of a state that affects a common payoff function, while the other agent either knows the past realizations of nothing about the state. In both cases, the second agent is assumed to have strictly causal observations of the first agent's actions, which enables the two agents to coordinate. These scenarios are applied to distributed power control; the key idea is that a transmitter may embed information about the wireless channel state into its transmit power levels so that an observation of these levels, e.g., the signal-to-interference-plus-noise ratio, allows the other transmitter to coordinate its power levels. The main contributions of this paper are twofold. First, we provide a characterization of the set of feasible average payoffs when the agents repeatedly take long sequences of actions and the realizations of the system state are i.i.d.. Second, we exploit these results in the context of distributed power control and introduce the concept of coded power-control. We carry out an extensive numerical analysis of the benefits of coded power control over alternative power-control policies, and highlight a simple yet non-trivial example of a power control code.