Model performance comparison.

Best performance for each test is italicized. First four rows are performance on 32,614 predictions of period one actions and 135,772 predictions of period greater than one actions. Each evaluation is an average for how that model performed with out-of-sample predictions for each game structure. We conduct paired sample t-tests (not assuming equal variances) to determine if the thirty accuracy and likelihood values for the full model are statistically greater than the values of the next best model. Accuracies for t>1 of the full model (p = 0.03) and the likelihoods for t>1 of the full model (p < 0.001) are significantly higher than the next best model (dynamic). Accuracies for t = 1 of the full model are greater than the next best model, the static model (p = 0.07), while the likelihoods for t = 1 of the full model are not significantly greater than the likelihoods of the static model (p = 0.31). Last four rows are performance on average cooperation level in each structure (n = 30) and time series of average cooperation in each structure (n = 212). Infinitely repeated interactions with delta set to 0.5 are on average only two periods long and there is not sufficient empirical data to extend out to eight periods so we extend to seven. Two structures are finitely repeated for two periods and two others are finitely repeated for four periods. We conducted paired sample t-tests between the full model and competitors, with a null hypothesis that the true difference in means of the 212 squared errors between predicted and real cooperation levels at all times in all game structures is equal to zero, i.e. that the full model and a competitor are statistically indistinguishable in terms of squared errors on time series predictions. We did the same for the thirty predictions of overall cooperation levels. We reject the null of no difference for all comparisons except with the static model for both tests and the dynamic model for the time series (see S1 Appendix).