Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control
<|reference_start|>Equilibrium Selection in Replicator Equations Using Adaptive-Gain Control: 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.<|reference_end|>
@article{zino2024equilibrium,
    title={Equilibrium Selection in Replicator Equations Using Adaptive-Gain
  Control},
    author={Lorenzo Zino and Mengbin Ye and Giuseppe Carlo Calafiore and
  Alessandro Rizzo},
    journal={arXiv preprint arXiv:2407.09305},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.09305},
    primaryClass={eess.SY cs.SY math.DS math.OC}
}