order to investigate how logistic regression compares against our agents’ naive approach, as a technique for estimating the current strategy weights, we will use it to estimate the current rock weight given a finite memory sample.

Letting $t_{ik}$ be the time at which agent $i$ experiences his $k$th interaction back from the current time, and $I_R(i,k)$ be the indicator function that this interaction is with a rock agent, then the likelihood of his current memory will be $$\mathcal{L}_i := \prod_{k=1}^{m} r(t_{ik})^{I_R(i,k)}[1-r(t_{ik})]^{1-I_R(i,k)}.$$ We now suppose that during the period of time covered by the agent’s memory, the rock probability weight may be expressed as a logistic function $$\label{rlogit}
r(t) = \frac{1}{1+e^{-(\beta_0 + \beta_1 t)}}$$ where $\beta_0$ and $\beta_1$ are constants. It is straightforward to carry out higher order regression where the exponent in the denominator is replaced with a polynomial of higher order. However, the length of time covered by agents’ memory will typically be significantly shorter than the period of oscillation, so that $r(t)$ changes in an approximately linear way whilst their samples are being collected. For example the period of oscillation in Figure \[hopf\] is $T \approx 1375$ whereas the memory length is $m=100$, and the greatest change in 