Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control

Autor:	Zino, Lorenzo, Ye, Mengbin, Calafiore, Giuseppe Carlo, Rizzo, Alessandro
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Dynamical Systems Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: Under Review
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.09305 Zobrazit plný text záznamu View this record from Arxiv