Compressed Sensing: a Novel Polynomial Complexity Solution to Nash Equilibria in Dynamical Games

Nash equilibria have been widely used in cognitive radio systems, sensor networks, defense networks and gene regulatory networks. Although solving Nash equilibria has been proved difficult in general, it is still desired to have algorithms for solving the Nash equilibria in various special cases. In this paper, we propose a compressed sensing based algorithm to solve Nash equilibria. Such compressed sensing method provides us a polynomial algorithm allowing more general payoff functions for certain classes of 2-player dynamic game. We also provide numerical examples to demonstrate the efficiency of proposed compressed sensing based method in solving Nash equilibria of 2-player games compared to existing algorithms.