Stability and Stabilization of Nash Equilibrium for Uncertain Noncooperative Dynamical Systems With Zero-Sum Tax/Subsidy Approach
提出一种零和税收/补贴方法，在无需代理人个人敏感参数信息的情况下，稳定伪梯度非合作动力系统中不稳定的纳什均衡，并通过数值例子验证其有效性。
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.