Stability and Stabilization of Nash Equilibrium for Uncertain Noncooperative Dynamical Systems With Zero-Sum Tax/Subsidy Approach

A zero-sum tax/subsidy approach for stabilizing unstable Nash equilibria in pseudo-gradient-based noncooperative dynamical systems is proposed without the information of agents’ personal sensitivity parameters. Specifically, we first present several sufficient conditions for guaranteeing stability of an unstable Nash equilibrium in the face of uncertainty. Furthermore, we develop a framework where a system manager constructs a zero-sum tax/subsidy incentive structure by collecting taxes from some agents and giving the same amount of subsidy in total to other agents so that the agents’ payoff structure is properly modified. Finally, we present several numerical examples to illustrate the utility of the zero-sum tax/subsidy approach.