Cyclical behavior of evolutionary dynamics in coordination games with changing payoffs

The paper presents a model of two-speed evolution in which the payoffs population game (or, alternatively, individual preferences) slowly adjust to changes aggregate behavior population. investigates how, for myopic agents with homogeneous preferences, environment caused by current may affect future and hence alter behavior. interaction between is based on symmetric two-strategy positive externalities negative feedback from payoffs, so that at every point time has an incentive coordinate, whereas over more popular strategy becomes less appealing. Under best response dynamics logit small noise levels joint trajectories preferences converge closed orbits around unique steady state, large state sink. replicator system repelling are unbounded unstable spirals.