On Distributed Nash Equilibrium Computation: Hybrid Games and a Novel Consensus-Tracking Perspective

Abstract

With the incentive to solve Nash equilibrium computation problems for networked games, this article tries to find answers for the following two problems: 1) how to accommodate hybrid games, which contain both continuous-time players and discrete-time players? and 2) are there any other potential perspectives for solving continuous-time networked games except for the consensus-based gradient-like algorithm established in our previous works? With these two problems in mind, the study of this article leads to the following results: 1) a hybrid gradient search algorithm and a consensus-based hybrid gradient-like algorithm are proposed for hybrid games with their convergence results analytically investigated. In the proposed hybrid strategies, continuous-time players adopt continuous-time algorithms for action updating, while discrete-time players update their actions at each sampling time instant and 2) based on the idea of consensus tracking, the Nash equilibrium learning problem for continuous-time games is reformulated and two new computation strategies are subsequently established. Finally, the proposed strategies are numerically validated.