Frequency-dependent strategy selection in a hunting game with a finite population

This paper considers a hunting game in the “playing the field” model, in which an individual within a group has to choose from two survival strategies: the group hunting strategy or the individual hunting strategy. The group hunting strategy aims at hunting more dangerous, larger prey, that are far beyond a single individual’s capture ability, where the return is greater but the risk is higher. While the individual hunting strategy aims at hunting small prey that can be easily captured by an independent individual, where the return is less but the risk is lower. Evolutionary game theory is used to investigate the selection dynamics of a two-strategy game with a finite population. This reveals the existences of the stable/unstable equilibrium points and evolutionarily stable strategies when there is the frequency-dependent strategy selection in the hunting game. The evolutionarily stable state is found to be not always unique because the system of the hunting game can have multiple equilibrium points. It is shown that a stable equilibrium point will always act as an evolutionarily stable strategy, while an unstable equilibrium point cannot resist invasion from a mutation. The population fitness cannot always reach the optimum level when applying the evolutionary process with the fitness difference function.