Stability and Stabilization of Nash Equilibrium for Uncertain Noncooperative Dynamical Systems With Zero-Sum Tax/Subsidy Approach
Stability and Stabilization of Nash Equilibrium for Uncertain Noncooperative Dynamical Systems With Zero-Sum Tax/Subsidy Approach
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DOI：
10.1109/tcyb.2022.3154109
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发表时间：
2022-09
影响因子：
11.8
通讯作者：
Yuyue Yan;T. Hayakawa
中科院分区：
文献类型：
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作者：
Yuyue Yan;T. Hayakawa
针对基于伪梯度的非合作动力系统，提出了一种零和税收/补贴方法，该方法在不需要个体敏感性参数信息的情况下稳定不稳定Nash均衡.具体来说，我们首先提出了几个充分条件，保证稳定的不稳定纳什均衡面对的不确定性。此外，我们开发了一个框架，系统管理者构建了一个零和税收/补贴的激励结构，从一些代理人征税，并给予相同数量的补贴总额给其他代理人，使代理人的支付结构得到适当的修改。最后，我们提出了几个数值例子来说明零和税收/补贴方法的效用。
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.