  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.
