The memory of each agent represents a sample from a time varying population, which is used to estimate the current properties of the population. It is the fact that the sample is not drawn from the current population which allows oscillations to form. Since the primitive method used by our agents to estimate strategy fractions plays a role in destabilizing the fixed point, it is interesting to compare it to more sophisticated methods in order to determine its plausibility as the choice of an agent with some degree of “common sense”, assuming he can recall the times at which the interactions in his sample took place. We do not formally address the question of which estimation technique would be selected by rational agents with unlimited intellectual resources.

In the same way that the method of regression is used to estimate, by maximum likelihood, the values of continuous explanatory variables given a sample of continuous response variables, so logistic regression [@Sha15] produces estimates when the response variables are discrete. The explanatory variables in our system are the collective time varying strategies of the group, whereas the response variables are the sequences of observations of strategy types that each agent makes. In 