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arXiv · 2306.14469

On Adaptive-Gain Control of Replicator Dynamics in Population Games

Lorenzo Zino·Mengbin Ye·Alessandro Rizzo·Giuseppe Carlo Calafiore
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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.

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Lorenzo Zino, Mengbin Ye, Alessandro Rizzo, Giuseppe Carlo Calafiore. 2023-06-26. On Adaptive-Gain Control of Replicator Dynamics in Population Games. https://doi.org/10.1109/cdc49753.2023.10383983

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