Distributed Nash Equilibrium Computation for Mixed-order Multi-player Games

Noticing that agents with different dynamics may work together, this paper considers Nash equilibrium computation for a class of games in which first-order integrator-type players and second-order integrator-type players interact in a distributed network. To deal with this situation, we firstly exploit a centralized method for full information games. In the considered scenario, the players can employ its own gradient information, though it may rely on all players' actions. Based on the proposed centralized algorithm, we further develop a distributed counterpart. Different from the centralized one, the players are assumed to have limited access into the other players' actions. Appropriate Lyapunov functions are constructed to investigate the effectiveness of the proposed methods analytically. It is shown that the proposed method would drive the players' actions to the Nash equilibrium exponentially. Lastly, the theoretical results are numerically verified by simulation examples.