This paper considers a version of the Hawk–Dove game of Maynard Smith and Price (1973) in which animals compete for a sequence of food items. Actions may depend on an animal's energy reserves. Costs and transition probabilities under a given policy depend on the mean level of aggressiveness, p, of the rest of the population. We find the optimal policy for a single animal under an average cost criterion when ρ is constant over time. We then consider the whole interacting population when individual members follow the same stationary policy. It is shown that the mean aggressiveness, p, asymptotically approaches a limiting value in this population. We then consider the existence of evolutionarily stable strategies for the population. It is shown that such strategies always exist but may not be unique.
