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Controlling evolutionary game-theoretic dynamics is a problem of paramountimportance for the systems and control community, with several applicationsspanning from social science to engineering. Here, we study a population ofindividuals who play a generic 2-action matrix game, and whose actions evolveaccording to a replicator equation -- a nonlinear ordinary differentialequation that captures salient features of the collective behavior of thepopulation. Our objective is to steer such a population to a specifiedequilibrium that represents a desired collective behavior -- e.g., to promotecooperation in the prisoner's dilemma. To this aim, we devise an adaptive-gaincontroller, which regulates the system dynamics by adaptively changing theentries of the payoff matrix of the game. The adaptive-gain controller istailored according to distinctive features of the game, and conditions toguarantee global convergence to the desired equilibrium are established.

On Adaptive-Gain Control of Replicator Dynamics in Population Games