On Adaptive-Gain Control of Replicator Dynamics in Population Games

TL;DR

This paper introduces an adaptive-gain controller for replicator dynamics in population games, enabling the steering of collective behavior towards desired equilibria by adaptively modifying the payoff matrix.

Contribution

It proposes a novel adaptive-gain control method tailored for replicator dynamics, with proven conditions for global convergence to target equilibria.

Findings

Controller guarantees convergence to desired equilibrium

Adaptive gain improves control effectiveness

Applicable to various 2-action 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.