Rager, CL; Bhat, U; Benichou, O; Redner, S

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 S 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 p = p* (S), the forager lives much longer than a normal forager that always eats when it encounters food. This optimal lifetime grows as S-2/ln S in one dimension and faster than a power law in S in two and higher dimensions.