Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909894437765120 |
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| author | Zino, Lorenzo Ye, Mengbin Calafiore, Giuseppe Carlo Rizzo, Alessandro |
| author_facet | Zino, Lorenzo Ye, Mengbin Calafiore, Giuseppe Carlo Rizzo, Alessandro |
| contents | In this paper, we deal with the equilibrium selection problem, which amounts to steering a population of individuals engaged in strategic game-theoretic interactions to a desired collective behavior. In the literature, this problem has been typically tackled by means of open-loop strategies, whose applicability is however limited by the need of accurate a priori information on the game and scarce robustness to uncertainty and noise. Here, we overcome these limitations by adopting a closed-loop approach using an adaptive-gain control scheme within a replicator equation -a nonlinear ordinary differential equation that models the evolution of the collective behavior of the population. For most classes of 2-action matrix games we establish sufficient conditions to design a controller that guarantees convergence of the replicator equation to the desired equilibrium, requiring limited a-priori information on the game. Numerical simulations corroborate and expand our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control Zino, Lorenzo Ye, Mengbin Calafiore, Giuseppe Carlo Rizzo, Alessandro Systems and Control Dynamical Systems Optimization and Control In this paper, we deal with the equilibrium selection problem, which amounts to steering a population of individuals engaged in strategic game-theoretic interactions to a desired collective behavior. In the literature, this problem has been typically tackled by means of open-loop strategies, whose applicability is however limited by the need of accurate a priori information on the game and scarce robustness to uncertainty and noise. Here, we overcome these limitations by adopting a closed-loop approach using an adaptive-gain control scheme within a replicator equation -a nonlinear ordinary differential equation that models the evolution of the collective behavior of the population. For most classes of 2-action matrix games we establish sufficient conditions to design a controller that guarantees convergence of the replicator equation to the desired equilibrium, requiring limited a-priori information on the game. Numerical simulations corroborate and expand our theoretical findings. |
| title | Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control |
| topic | Systems and Control Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2407.09305 |