Table 1. Free and fixed parameters of all six computational models.

	Delta rule		Bayes learner rule
Choice rule 1	$\alpha ,\beta$	fixed: $v_1$	$\beta$	fixed: ${\displaystyle \hat{\lambda },\hat{\vartheta },{\hat{\sigma }}_0^2,{\hat{\sigma }}_d^2,{\hat{\mu }}_1^{pre},{\hat{\sigma }}_1^{pre}}$
Choice rule 2	$\alpha ,\beta ,\phi$	fixed: $v_1$	$\beta ,\phi$	fixed: ${\displaystyle \hat{\lambda },\hat{\vartheta },{\hat{\sigma }}_0^2,{\hat{\sigma }}_d^2,{\hat{\mu }}_1^{pre},{\hat{\sigma }}_1^{pre}}$
Choice rule 3	$\alpha ,\beta ,\phi ,\rho$	fixed: $v_1$	$\beta ,\phi ,\rho$	fixed: ${\displaystyle \hat{\lambda },\hat{\vartheta },{\hat{\sigma }}_0^2,{\hat{\sigma }}_d^2,{\hat{\mu }}_1^{pre},{\hat{\sigma }}_1^{pre}}$
Choice rule 4	$\alpha ,\beta ,\phi ,\rho ,\gamma$	fixed: $v_1$	$\beta ,\phi ,\rho ,\gamma$	fixed: ${\displaystyle \hat{\lambda },\hat{\vartheta },{\hat{\sigma }}_0^2,{\hat{\sigma }}_d^2,{\hat{\mu }}_1^{pre},{\hat{\sigma }}_1^{pre}}$

Note: Free parameters are only listed for the subject-level. Hierarchical models contained for each free subject-level parameter $x$ two additional free parameters (${{\rm M}}^x,{\Lambda }^x$) on the group-level (Figure 9). Choice rule 1: softmax; Choice rule 2: softmax with exploration bonus; Choice rule 3: softmax with exploration bonus and perseveration bonus; $\alpha$: learning rate; $\beta$: softmax parameter; $\phi$: exploration bonus parameter; $\rho$: perseveration bonus parameter; $,\gamma$: uncertainty-based random exploration parameter; $v_1$: initial expected reward values for all bandits; $\widehat{\lambda }$: decay parameter; $\widehat{\vartheta }$: decay center; ${\widehat{\sigma }}_o^2$: observation variance; ${\widehat{\sigma }}_d^2$: diffusion variance; ${\widehat{\mu }}_1^{pre}$: initial mean of prior expected rewards for all bandits; ${\widehat{\sigma }}_1^{pre}$: initial standard deviation of prior expected rewards for all bandits.