equations.

The neurological mechanisms by which humans and animals remember information are not completely understood [@Tra10], but it is clear that there are multiple types of memory, and memory systems [@Mil98]. Broadly speaking, memories fall into two classes: they are either explicit recollections of events or facts - “declarative” memories - or learned motor or social skills and social conditioning [@Tra10]. Our agents are endowed with a simple, finite declarative memory for interactions, but our analysis could be repeated with other models of memory, or an empirical “forgetting curve” [@Ave10] which describes how memory decays with time. Our current aim is to investigate how the length of an agent’s memory can influence their individual effectiveness, and the dynamics of the game. In common with earlier investigations of the use of sampling to determine strategy updates [@Gal09], we find that sample size (memory length), which determines the strength of noise in the data, has a powerful effect. After demonstrating the appearance of limit cycles, we investigate how reduced noise aids decision making. Because each agent’s memory includes both recent and older behaviour, then strategy updates are made based on slightly out-of-date information. Provided that strategy adjustments are sufficiently small or, equivalently, 