Fixed-Time Consensus-Based Event-Triggered Nash Equilibrium Seeking Strategy

This brief studies Nash equilibrium (NE) seeking problems among groups of players in non-cooperative games. Instead of having global information, this group of players exchanges their information via a topology graph. By integrating the leader-follower consensus protocol with the gradient descent method, we design a new finite-time event-triggered NE seeking strategy. The NE is practical finite-time stable under the proposed algorithm, even though estimate updates occur only when the triggering condition is satisfied. Moreover, players’ estimates on the actions converge to sufficiently small circles centered at the actual actions in a fixed time, which can be predefined by adjusting the design parameters. The strictly positive inter-execution time is proven to reveal the inexistence of Zeno behavior. Lastly, a simulation is provided to demonstrate the feasibility and efficiency of the designed algorithm.