Robust Incentive Stackelberg Games With a Large Population for Stochastic Mean-Field Systems
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Bibliographic record
Abstract
A static output feedback (SOF) strategy for robust incentive Stackelberg games with a large population for mean-field stochastic systems is investigated. First, the saddle point equilibrium condition of external disturbance and control strategy is derived based on stochastic algebraic matrix equations (SAMEs). Then, a centralized SOF incentive Stackelberg strategy is derived through restructuring the follower’s strategies and the leader’s incentive strategy. Moreover, to avoid the high dimension of design procedure, a new designing algorithm of low-dimensional approximation SOF incentive Stackelberg strategy is proposed. It is shown that the difference in the equilibrium values between using the centralized SOF incentive Stackelberg strategy and using the low-dimensional approximation SOF incentive Stackelberg strategy is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(\sqrt {\varepsilon })=O(1/\sqrt {N})$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> denotes the population size. Finally, a numerical example with a large population size demonstrates the effectiveness of the proposed approximation SOF incentive Stackelberg strategy.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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