Beyond Nash Solutions for Differential Graphical Games

Differential graphical games model the interaction between networked dynamical agents that do not possess global state information available. In general, this lack of global information prevents the agents from playing their optimal Nash strategies. In this article, two different solution concepts for graphical games are proposed as practical alternatives when Nash equilibrium is not attainable among the players. The proposed solutions consider the case on which the players make optimistic assumptions about their neighbors, and are characterized by providing distributed, linear control policies. The robustness properties of each solution, in terms of the gain and phase margins, are also determined.