Distributed Nash Equilibrium Seeking on Compact Action Sets over Jointly Strongly Connected Switching Networks

This paper studies the distributed Nash equilibrium seeking (DNES) problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition. To keep the actions of all players in their action sets all the time, one has to resort to the projected gradient-based method. Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system, an algorithm is proposed that is able to exponentially find the Nash equilibrium. Further, the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets. Two examples are used to illustrate the proposed approach.