Prey should hide more randomly when a predator attacks more persistently

When being searched for and then (if found) pursued by a predator, a prey animal has a choice between choosing very randomly among hiding locations so as to be hard to find or alternatively choosing a location from which it is more likely to successfully flee if found. That is, the prey can choose to be hard to find or hard to catch, if found. In our model, capture of prey requires both finding it and successfully pursuing it. We model this dilemma as a zero-sum repeated game between predator and prey, with the eventual capture probability as the pay-off to the predator. We find that the more random hiding strategy is better when the chances of repeated pursuit, which are known to be related to area topography, are high. Our results extend earlier results of Gal and Casas, where there was at most only a single pursuit. In that model, hiding randomly was preferred by the prey when the predator has only a few looks. Thus, our new multistage model shows that the effect of more potential looks is opposite. Our results can be viewed as a generalization of search games to the repeated game context and are in accordance with observed escape behaviour of different animals.