Graphical Games: Distributed Multiplayer Games on Graphs

Abstract

In this chapter, it is seen that distributed control protocols that both guarantee synchronization and are globally optimal for the multi-agent team always exist on any sufficiently connected communication graph if a different definition of optimality is used. To this end, we study the notion of Nash equilibrium for multiplayer games on graphs. This leads us to the idea of a new sort of differential game—graphical games. In graphical games, each agent has its own dynamics as well as its own local performance index. The dynamics and local performance indices of each agent are distributed; they depend on the state of the agent, the control of the agent, and the controls of the agent’s neighbors. We show how to compute distributed control protocols that guarantee global Nash equilibrium for multi-agent teams on any graph that has a spanning tree.