  We model a situation in which a collection of species derive their fitnesses
via a rock-paper-scissors-type game; however, the precise payoffs are a
function of the environment. The new aspect of our model lies in adding a
feedback loop: the environment changes according to the relative fitnesses of
the species; in particular, it gives a boost to the species having small
populations. We cast our model in the setting of a differential game and we
show that for a certain setting of parameters, this dynamics cycles. Our model
is a natural one, since depletion of resources used by more frequent species
will shift the payoff matrix towards favoring less frequent ones. Since the
dynamics cycles, no species goes extinct and diversity is maintained.
