  Models in evolutionary game theory traditionally assume symmetric
interactions in homogeneous environments. Here, we consider populations
evolving in a heterogeneous environment, which consists of patches of different
qualities that are occupied by one individual each. The fitness of individuals
is not only determined by interactions with others but also by environmental
quality. This heterogeneity results in asymmetric interactions where the
characteristics of the interaction may depend on an individual's location.
Interestingly, in non-varying heterogeneous environments, the long-term
dynamics are the same as for symmetric interactions in an average, homogeneous
environment. However, introducing environmental feedback between an
individual's strategy and the quality of its patch results in rich
eco-evolutionary dynamics. Thus, individuals act as ecosystem engineers. The
nature of the feedback and the rate of ecological changes can relax or
aggravate social dilemmas and promote persistent periodic oscillations of
strategy abundance and environmental quality.
