Stochastic Approximation Based Tracking of Correlated Equilibria for Game-Theoretic Reconfigurable Sensor Network Deployment

Deployment of wireless sensors to efficiently forward information through a large array is considered from a game-theoretic perspective. Sensors with limited awareness learn to make local decisions (sleep/wake) in order to forward data in a slowly varying environment through a "regret matching" algorithm. With appropriately small smoothing and perturbation, we are able to apply results from stochastic approximation to establish global convergence of this algorithm and for an adaptive variant. The adaptive version allows sensor network connections to be reconfigured as game conditions change. We illustrate this reconfigurability with respect to channel fading, changing network demands, and sensor failure. Instead of the Blackwell approachability method used in previous papers, we give an ordinary differential equation formulation with a Lyapunov function to prove convergence to a correlated equilibrium. Numerical studies show that the algorithms can satisfactorily track correlated equilibria in systems of several thousand sensors, resulting in near competitive optimality at each sensor