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arXiv · 2407.09305

Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control

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

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.

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BibTeXRIS

Lorenzo Zino, Mengbin Ye, Giuseppe Carlo Calafiore, Alessandro Rizzo. 2024-07-12. Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control. https://doi.org/10.1109/tac.2025.3567253

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