Pursuit and an evolutionary game

Pursuit is a familiar mechanical activity that humans and animals engage in-athletes chasing balls, predators seeking prey and insects manoeuvring in aerial territorial battles. In this paper, we discuss and compare strategies for pursuit, the occurrence in nature of a strategy known as motion camouflage, and some evolutionary arguments to support claims of prevalence of this strategy, as opposed to alternatives. We discuss feedback laws for a pursuer to realize motion camouflage, as well as two alternative strategies. We then set up a discrete-time evolutionary game to model competition among these strategies. This leads to a dynamics in the probability simplex in three dimensions, which captures the mean-field aspects of the evolutionary game. The analysis of this dynamics as an ascent equation solving a linear programming problem is consistent with observed behaviour in Monte Carlo experiments, and lends support to an evolutionary basis for prevalence of motion camouflage.