interactions, producing a sample from the population of strategies $\{R,S\}$ where $R$ and $S$ are the numbers of rock and scissors interactions in his memory. Note that at any given time, both samples $\{R,S\}$ and strategies $[r_i,s_i]_n$ require only two parameters for their description.

Agents estimate the current average probability weights of their opponents as the fractions in their current sample, and use this to discern the optimal strategy. From the form of the payoff matrix (\[POM\]), we see that the optimal strategy is determined by which of the following domains the current sample lies $$\begin{aligned}
\label{RDom}
\mathcal{D}_{R} & := \left\{ S > \frac{\gamma m}{\alpha + \beta+ \gamma} , R > \frac{(\beta+\gamma)m}{\alpha + \beta + \gamma} - S \right\}  \\
\label{SDom}
\mathcal{D}_{S} & := \left\{ R < \frac{\beta m}{\alpha + \beta + \gamma} , R < \frac{(\beta+\gamma)m}{\alpha + \beta + \gamma} - S \right\} \\
\label{PDom}
\mathcal{D}_{P} & := \left\{ R > \frac{\beta m}{\alpha + \beta + \gamma} , S < \frac{\gamma m}{\alpha + \beta + \gamma} \right\}.\end{aligned}$$ These domains are illustrated in Figure \[rspDoms\].

![Domains in which each of the three strategies are assessed to be the best. \[rspDoms\]](RSPDoms.eps){width="6cm"}

At each point in time, each agent’s memory defines the 