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.
On Adaptive-Gain Control of Replicator Dynamics in Population Games / Zino, Lorenzo; Ye, Mengbin; Rizzo, Alessandro; Calafiore, Giuseppe Carlo. - ELETTRONICO. - (2023), pp. 485-490. (Intervento presentato al convegno 2023 62nd IEEE Conference on Decision and Control (CDC) tenutosi a Singapore (Singapore) nel 13-15 Dicembre 2023) [10.1109/CDC49753.2023.10383983].
On Adaptive-Gain Control of Replicator Dynamics in Population Games
Zino, Lorenzo;Rizzo, Alessandro;Calafiore, Giuseppe Carlo
2023
Abstract
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.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2985305