Recently, game theory has been proposed as a tool for cooperative control. Specifically, the interactions of a multi-agent distributed system are modeled as a non-cooperative game where agents are self-interested. In this work, we prove that this approach of non-cooperative control has limitations with respect to engineering multi-agent systems. In particular, we prove that it is not possible to design budget balanced agent utilities that also guarantee that the optimal control is a Nash equilibrium. However, it is important to realize that game-theoretic designs are not restricted to the framework of non-cooperative games. In particular, we demonstrate that these limitations can be overcome by conditioning each player's utility on additional information, i.e., a state. This utility design fits into the framework of a particular form of stochastic games termed state-based games and is applicable in many application domains.
['Jason R. Marden', 'Adam Wierman']
Overcoming limitations of game-theoretic distributed control