Compressed-sensing game theory (CSGT): A novel polynomial complexity solution to Nash equilibria in dynamical games

Game-theoretic methods based on Nash equilibria have been widely used in various fields including signal processing and communication applications such as cognitive radio systems, sensor networks, defense networks and gene regulatory networks. Solving the Nash equilibria, however, has been proven to be a difficult problem, in general. It is therefore desired to obtain efficient algorithms for solving the Nash equilibria in various special cases. In this paper, we propose a Compressed-Sensing Game Theory (CSGT) framework to solve the Nash equilibria. We demonstrate that the proposed CSGT framework provides a polynomial complexity solution to the Nash Equilibria, thus allowing more general pay-off functions for certain classes of two-player dynamic games. We also provide numerical examples that demonstrate the efficiency of proposed CSGT framework in solving the Nash equilibria for two-player games in comparison to existing algorithms.