On Adaptive-Gain Control of Replicator Dynamics in Population Games
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917809261379584 |
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| author | Zino, Lorenzo Ye, Mengbin Rizzo, Alessandro Calafiore, Giuseppe Carlo |
| author_facet | Zino, Lorenzo Ye, Mengbin Rizzo, Alessandro Calafiore, Giuseppe Carlo |
| contents | Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals who play a generic 2-action matrix game, and whose actions evolve according to a replicator equation -- a nonlinear ordinary differential equation that captures salient features of the collective behavior of the population. Our objective is to steer such a population to a specified equilibrium that represents a desired collective behavior -- e.g., to promote cooperation in the prisoner's dilemma. To this aim, we devise an adaptive-gain controller, which regulates the system dynamics by adaptively changing the entries of the payoff matrix of the game. The adaptive-gain controller is tailored according to distinctive features of the game, and conditions to guarantee global convergence to the desired equilibrium are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14469 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Adaptive-Gain Control of Replicator Dynamics in Population Games Zino, Lorenzo Ye, Mengbin Rizzo, Alessandro Calafiore, Giuseppe Carlo Systems and Control Dynamical Systems Optimization and Control Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals who play a generic 2-action matrix game, and whose actions evolve according to a replicator equation -- a nonlinear ordinary differential equation that captures salient features of the collective behavior of the population. Our objective is to steer such a population to a specified equilibrium that represents a desired collective behavior -- e.g., to promote cooperation in the prisoner's dilemma. To this aim, we devise an adaptive-gain controller, which regulates the system dynamics by adaptively changing the entries of the payoff matrix of the game. The adaptive-gain controller is tailored according to distinctive features of the game, and conditions to guarantee global convergence to the desired equilibrium are established. |
| title | On Adaptive-Gain Control of Replicator Dynamics in Population Games |
| topic | Systems and Control Dynamical Systems Optimization and Control |
| url | https://arxiv.org/abs/2306.14469 |