The advantage of foraging myopically. (16th July 2018) - Rager, C L; Bhat, U; Bénichou, O; Redner, S
Abstract: We study the dynamics of a myopic forager that randomly wanders on a lattice in which each site contains one unit of food. Upon encountering a food-containing site, the forager eats all the food at this site with probability p   <  1; otherwise, the food is left undisturbed. When the forager eats, it can wander additional steps without food before starving to death. When the forager does not eat, either by not detecting food on a full site or by encountering an empty site, the forager goes hungry and comes one time unit closer to starvation. As the forager wanders, a multiply connected spatial region where food has been consumed—a desert—is created. The forager lifetime depends non-monotonically on its degree of myopia p, and at the optimal myopia, the forager lives much longer than a normal forager that always eats when it encounters food. This optimal lifetime grows as in one dimension and faster than a power law in in two and higher dimensions.