Dynamic coordination of multiple agents in a class of differential games through a generalized linear reward scheme

We consider a wide class of dynamic problems characterized by multiple, non-cooperative agents operating under a general control rule. Since each agent follows its own objective function and these functions are interdependent, control efforts made by each agent may affect the performance of the other agents and thus affect the overall performance of the system. We show that recently developed dynamic linear reward/penalty schemes can be generalized to provide coordination of the multiple agents in a broad-spectrum dynamic environment. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution even though they operate in a decentralized decision-making environment.