State-dependent contests for food

Abstract

We consider a population in which the animals differ in their level of energy reserves. A pair of animals from this population contest an item of food. We investigate the evolutionarily stable strategies in the contest. Rather than assuming a set of costs and benefits, we suppose that the animals return to a background foraging process after the contest. This approach allows us to derive the costs and benefits directly in terms of the animal's expected future reproductive success. In a state-dependent version of the Hawk-Dove game, animals should play Hawk if their reserves are low and play Dove if their reserves are high. In a state-dependent version of the War of Attrition game, the situation is less clear. This is because although both the value of a food item and the cost of wasting time change with reserves, they remain roughly proportional to one another. When these benefits and costs are exactly proportional to one another we show that there is no evolutionarily stable strategy, and that the obvious negative exponential strategy can be invaded by two classes of policy. In one class, animals become more persistent as the value of food increases; in the other class animals become less persistent as the value of food increases. In both cases the mutant policy invades because although it does badly against the resident population when rewards and costs are low, it does well against the resident population when rewards and costs are high.