*7.1. Memory*

We explore to what extent adding memory explains behavior in CBL. This is an important part of our depiction of learning, and we test the regularity to which it is important by varying the known memory of subjects in CBL. Figure 4 shows the improvement in the mean quadratic score as more memory is allowed in the CBL algorithm starting with three prior periods in memory (*M* = 3) and expanding to seventeen prior periods (*M* = 17). If we refer to three periods in memory, then subjects 'forget' periods that were further in the past than three periods (rounds) ago and do not consider them in comparing the current periods definition of a case. The figure demonstrates that increasing the length of short time-horizons provide an improvement in model fit, but most gains are exhausted by around nine periods. Because period number is included as an element of the problem definition P, continuing to add more periods into the similarity function makes little difference past nine periods and degrades past fifteen periods. This provides the basis of our choice of fifteen periods for estimation.

**Figure 4.** Length of Memory *M*.
