Wardrop Equilibrium and Potential Games in Wireless

We investigate the relevance of application of game theory to the field of wireless ad-hoc networks. We give distributed algorithms for routing and multihoming in wireless ad-hoc networks. We propose a distributed routing scheme for a broad class of wireless ad-hoc networks which converges (in the Cesaro sense) to the set of Cesaro-Wardrop equilibria. Convergence is established by formulating a potential game and by showing the existence of a potential function. Stochastic approximation used by us converges to replicator dynamics and replicator dynamics possess Positive Correlativity. Existence of potential function and positive correlativity of evolutionary dynamics ensures that all nash equilibria are stationary points of replicator dynamics. We also propose a distributed algorithm for multihoming. We give a two time-scale approximation scheme in which channel access probabilities are learned on a faster timescale and association to the available access points is changed and learned on a slower timescale. We give a stochastic approximation scheme for learning channel access probabilities by defining a game. Payoffs in the game are set in such a way so that a global optimization problem is solved in a distributed manner. In a continuous time limit, learning model for the association of users to access points, converges to the replicator dynamics of evolutionary game theory. We define that system has reached wardrop equilibrium if each user gets equal probability of successful transmission regardless of which access point it is associated with.