After the seminal work of Nowak and May (1992), the Spatial Prisoner’s Dilemma has become a common metaphor for studying the dynamics of cooperation in a spatially structured population. In contrast to the widely employed evolutionary model, which studies the dynamics of cooperation in a population of primitive players that lack memory, this paper examines the problem of cooperation in a population of memory-based players. Using computational simulations, it is shown that partial cooperation is maintained in a spatially structured population of players whose decision-making is effectuated by the adaptive nature of memory embodied in the ACT-R cognitive architecture (Anderson & Lebiere, 1998).