On Adaptive-Gain Control of Replicator Dynamics in Population Games
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.
Keywords
Cite
@article{arxiv.2306.14469,
title = {On Adaptive-Gain Control of Replicator Dynamics in Population Games},
author = {Lorenzo Zino and Mengbin Ye and Alessandro Rizzo and Giuseppe Carlo Calafiore},
journal= {arXiv preprint arXiv:2306.14469},
year = {2024}
}
Comments
6 pages, Accepted for presentation at the 2023 IEEE CDC