Stability and Stabilization of Nash Equilibrium for Uncertain Noncooperative Dynamical Systems With Zero-Sum Tax/Subsidy Approach
- Resource Type
- Periodical
- Authors
- Yan, Y.; Hayakawa, T.
- Source
- IEEE Transactions on Cybernetics IEEE Trans. Cybern. Cybernetics, IEEE Transactions on. 52(11):11287-11298 Nov, 2022
- Subject
- Signal Processing and Analysis
Communication, Networking and Broadcast Technologies
Robotics and Control Systems
General Topics for Engineers
Components, Circuits, Devices and Systems
Computing and Processing
Power, Energy and Industry Applications
Nash equilibrium
Sensitivity
Finance
Uncertainty
Game theory
Economics
Compensation by incentives
gradient play
noncooperative system
stabilization
tax/subsidy approach (TSA)
- Language
- ISSN
- 2168-2267
2168-2275
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.