Solving potential games with unstable dynamics

We solve N-player potential games with possibly unstable dynamics in this paper. Different from most of the existing Nash seeking methods, we provide a method based on an extremum seeking scheme that does not require the information on the game dynamics or the payoff functions. Only measurements of the payoff functions are needed in the game strategy synthesis. Compared with other Nash equilibrium seeking methods based on extremum seeking which are model free as well, we don´t need the dynamics of the potential games to be stable. The game dynamics can even be non-autonomous. Lie bracket approximation is used for the analysis of the proposed scheme and a semi-globally practically uniformly ultimately bounded result is given. Stability of the closed loop system is verified and the ultimate bound is quantified. A numerical example is presented to validate the proposed method. The main contribution of the paper is that the proposed method can achieve stabilization and Nash equilibrium seeking for potential games with non-autonomous dynamics that may be unstable while no explicit model information is required.