Game-driven random walks: Survival time statistics.

Random walks are most universal tool to describe and analyze complex spatio-temporal activity of living beings, ranging from cells to humans. Most of such processes are not truly random but are results of a complex multilayered combination of cognitive processes and decision making -- foraging, search for a mate, mapping of a new territory. Here we consider a walk process in a two-dimensional domain driven by a game in which players pursuit the opposite aims: one wants to stay as long as possible within the domain while another one wants to reach the adsorbing border as fast as possible.