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