Spatial order prevails over memory in boosting cooperation in the iterated prisoner's dilemma.

This paper presents some results on a spatial version of the iterated prisoner's dilemma in which every player imitates in any iteration the optimal strategy of its neighbors. Neighbors are defined with different degrees of random variation (initial rewiring) based on a square lattice, and optimal is defined with different degrees of memory, ranging from only the single preceding iteration up to all preceding iterations. It is concluded that memory notably stimulates cooperation in the iterated prisoner's dilemma played in ordered lattices, but it is unable to boost cooperation as the wiring network becomes highly disordered.