Fast Seeking of Nash Equilibria without Steady-State Oscillation in Games with Non-Quadratic Payoffs

In this paper, a solution for Nash equilibrium seeking problem for N-players static non-cooperative games with non-quadratic payoff functions is proposed. The proposed solution is a non-model based approach, in the sense that the players do not need any knowledge about the agent's model or other players' actions, and can attain the Nash equilibrium using only measurements of payoff values. To overcome the shortcoming of existing non-model based algorithms, for which the Nash equilibrium stays within a small neighborhood and oscillates, the proposed approach adjusts the classical extremum seeking algorithms so that the amplitude of excitation sinusoidal signal converges to zero locally and exponentially. Therefore, with removing steady-state oscillation, not only the deleterious effects of steady-state oscillation is eliminated but also Nash equilibrium is achieved faster. The details of proof and the analysis for stability and convergence are provided. Finally, the efficiency and effectiveness of the algorithm are illustrated with a numerical example and simulation.