A Further details for the two-step task analyses

A.1 Parameter recovery To assess the estimability/identifiability of the model parameters, we performed a parameter recovery analysis (Supplemental Figure 1). New data were generated from the model based on participants' parameters (referred to as'generative') and the model was re-estimated on these data. The rank correlation between the generative and re-estimated (or'recovered') parameters was greater than 0.74 (for all parameters except for the dispersion parameter, η Correlations were all highly significant (p < 1e 10), as shown by the 95%-confidence intervals around the regression lines. There are two small differences between our model and theirs. One difference is that the model in [1] uses both rewards and the intermediate values from stage 2 to estimate the values in stage 1 (equation 5).