Distributed Nash equilibrium seeking strategy with incomplete information

Abstract

In this paper, two kinds of distributed Nash equilibrium seeking strategies based on Kalman filter are proposed in non-cooperative games with incomplete information. In the discrete-time system with process and measurement noises, each player, selfish and only considering its own profit, utilizes the gradient method to maximize the benefit. Since the payoff function is related to all players' states, Kalman filter and leader-following consensus are used to estimate the states in the network. Furthermore, considering the trade-off between strategy precision of Nash equilibrium and communication rate, another Nash equilibrium seeking method is proposed by introducing an event-based scheduler. The convergence of both Nash equilibrium seeking strategies is analyzed based on Lyapunov method. It is proved that both strategies are bounded in the mean square sense. Simulation examples are given to verify the efficiency.

Keywords: Event-based scheduler; Incomplete information; Kalman filter; Nash equilibrium; Non-cooperative game.