Distributed Finite-Time Nash Equilibrium Seeking for Non-Cooperative Games

The paper aims to design a distributed algorithm for players in games such that the players can learn Nash equilibriums of non-cooperative games in finite time. We first consider the quadratic non-cooperative games and design estimate protocols for the players such that they can estimate all the other players’ actions in distributed manners. In order to make the players track all the other players’ real actions in finite time, a bounded gradient dynamics is designed for players to update their actions by using the estimate information. Then the algorithm is extended to more general non-cooperative games and it is proved that players’ estimates can converge to all the other players’ real actions in finite time and all players can learn the unique Nash equilibrium in finite time under mild assumptions. Finally, simulation examples are provided to verify the validity of the proposed finite-time distributed Nash equilibrium seeking algorithms.