Strategy, compromise, and cheating in predator–prey games

Background: A prey’s optimal level of anti-predator behaviour depends on its hunger state and its assessment of danger in the environment. Similarly, a predator’s optimal attack behaviour depends on its own satiation level and its assessment of the risks and costs associated with hunting. The optimal behaviour of each depends on what the other is doing, resulting in a dynamic game. Assumptions: We assume that predators are more successful at hunting their prey when prey are further from safety, and that prey are more successful in finding their food items in more risky environments. Question: Under these assumptions, what is the evolutionarily stable strategy (ESS) and how does it respond to false attacks by the predators? Mathematical methods: We use stochastic dynamic programming to compute the probabilities of prey and predators surviving a foraging season (e.g. the winter) and game theoretical methods to compute the evolutionarily stable strategies. Results: We find the ESS, and we demonstrate that when foraging time is limited, a predator benefits from making extra ‘false’ attacks on the prey, assuming it can do so safely and efficiently. The extra attacks disturb the prey until they can no longer afford the time for anti-predator behaviour and become easier targets during the next ‘real’ attack.