Nash Equilibrium Topology of Multi-Agent Systems With Competitive Groups

Competition is ubiquitous in nature. This paper studies competition phenomena of multi-agent systems consisting of three groups of agents. In order to achieve maximal influence, the first and the second groups send information to the third group, which leads to competition. First, we formulate this competition as a noncooperative game in which the first and the second groups are two players. Players decide agents who send and receive information. Consequently, the interaction topology of the system is generated from players' strategies. Therefore, we define the interaction topology decided by Nash equilibrium of the game as the equilibrium topology of the system. Second, the necessary condition is established for equilibrium topology. For the case that the third group's interaction graph is a tree or has a center vertex, interchangeable Nash equilibrium solutions are obtained. Moreover, due to competition, the agents of the third group might reach consensus under the equilibrium topology. Finally, when the third group's interaction graph is bidirected, the necessary and sufficient condition is given for the equilibrium topology. The equilibrium topology is also presented for the scenario where the third group's interaction graph is a bidirected circulant graph.