The Spatialized, Continuous‐Valued Battle of the Sexes

The dynamics of a spatial, continuous‐valued formulation of the iterated battle of the sexes is assessed in this work. The game is played in the cellular automaton manner, i.e., with local and synchronous interaction. The effects of probabilistic updating and memory of past encounters are also taken into account. With deterministic updating, the spatial structure enables the emergence of coordination clusters, leading to the mean payoffs per encounter to values that are accessible only in the cooperative two‐person game scenario, which constitutes a notable case of self‐organization. With probabilistic updating of choices, both kinds of player tend to reach a full coordination absorbing steady state in the long term. As a general rule, short‐term memory of past iterations does not qualitatively alter the ahistoric dynamics. Unlimited trailing memory induces an inertial effect that alters the dynamics to a larger extent, particularly in the probabilistic updating scenario, in which case unlimited trailing memory fully inhibits the dynamics.