A distributed method for simultaneous social cost minimization and nash equilibrium seeking in multi-agent games

In this paper, a fully distributed strategy is proposed to solve the N-coalition multi-agent games. The agents in the considered N-coalition multi-agent games are supposed to have limited access to the other players' actions. Consensus protocols, including a leader-following consensus protocol and a dynamic average consensus protocol, are leveraged to search for the Nash equilibrium of the N-coalition multi-agent games. In particular, the leader-following consensus protocol is employed to estimate the agents' actions and the dynamic average consensus protocol is employed to deal with the social cost minimization problem in each coalition. Analytical convergence result is derived under certain conditions by utilizing Lyapunov stability analysis.