Existence of Feasible Provisional Transfer-Based Tax/Subsidy Approach for Stabilizing Noncooperative Dynamical Systems: Graph Analysis

A provisional transfer-based zero-sum tax/subsidy approach is characterized to stabilize a Nash equilibrium for the noncooperative dynamical systems with unknown sensitivity parameters. In the proposed approach, the system designer establishes a transfer graph between agents and modifies agents' payoff functions by collecting taxes from some agents and giving the same amount as subsidy to a neighbor corresponding agent(s) in the transfer graph. To achieve the zero-sum tax/subsidy approach with provisional transfer where there is no adjustment at the moment when the approach executes nor the moment when the Nash equilibrium is reached, some typical topologies of transfer graphs where the provisional transfer-based zero-sum tax/subsidy approach exists are presented.