position of a random walker in the simplex $\{(R,S) | R+S \leq m\}$, with each new interaction determining the next step of the walk. After each step an agent will update his strategy according to the domain in which its memory lies, using the following rule $$[r_i,s_i]_{n+1} = (1-\epsilon) [r_i,s_i]_n + \epsilon
\begin{cases}
 [1,0] \text{ if } (R,S) \in \mathcal{D}_R \\
 [0,1] \text{ if } (R,S) \in \mathcal{D}_S \\
 [0,0] \text{ if } (R,S) \in \mathcal{D}_P.
\end{cases}
\label{EMA}$$ For certain combinations of payoffs and memory length, $(R,S)$ can lie on the boundary between two domains, in which case no update is made. The parameter $\epsilon \in [0,1]$, the “update rate”, describes the sensitivity of agents to new information, and $n$ indexes the number of interactions. According to definition (\[EMA\]), the current strategy is an exponential moving average of the strategies which were estimated to be optimal from past interactions. Our learning rule has some commonality with experience weighted attraction rules used in recent studies [@Gal09; @Gal13] where a parameter analogous with our $\epsilon$ is used to describe how rapidly agents respond to new information. In these studies, the parameter is interpreted as a measure of memory in the learning process, 