**8. Empirical Comparison of Learning Models**

In this section, we investigate the dynamics of RL and CBL, the two best-fitting learning models, to more fully understand the results of these learning algorithms. Previously we discussed the potential overlap in RL and CBL, which in practice have similar fits to the data. CBL likely outperforms RL in aggregate due to its ability to incorporate important information in the the choice behavior of subjects. RL and CBL appear to converge on choices overtime. We illustrate convergence in prediction between CBL and RL in Figure 5. There is a possibility that RL and CBL are increasingly correct about different types of individual decisions and could not actually be converging to similar predictions of behavior. For example, say there are three types of decision makers (A, B, and C). CBL and RL predict players of type A well, but not B or C. As more information is added and the learning models improve goodness of fit, CBL predicts player type B better and RL predicts player type C better. Both of the models are doing better, but are doing it on different observations and therefore on not converging on the types of predictions they get correct. The convergence between CBL and EWA by round in Figure 5 demonstrates that the gains in accuracy are accompanied by a convergence in agreement between the two learning algorithms, although convergence is slight. The coefficient of the regression line in Figure 5 is −0.00006 with a clustered standard error by game type of 0.00002. This coefficient is statistically significant with a t-statistic of −2.98.

We also provide the model fits by individual games in Appendix D. Table A3 and A4 show the in-sample and out-of-sample model fits by individual game for all learning models.

**Figure 5.** Convergence of RL and CBL. The red line denotes an OLS regression line of round on percent difference in predictions.
