Skip to main content
Figure 4 | EPJ Data Science

Figure 4

From: Optimal prediction of decisions and model selection in social dilemmas using block models

Figure 4

Mixed-strategy model. (a) Predictive accuracy of the multiple-strategy model (green) as a function of the game aggregation factor α. We show results for \(K=3\) latent groups of players and \(L=4\) latent groups of games; increasing the number of groups did not result in an increase in accuracy (see Fig. S3). Each point represents the average of a 5-fold cross-validation; error bars indicate the standard error of the mean. Grey symbols represent the predictive accuracy of the single-strategy model as in Fig. 2(a), and the solid black line represents the accuracy of the baseline model. (b)–(e) Top group memberships for each game (top), distribution of the entropies of player membership vectors (middle), and cooperation matrices p (bottom) for each of the values \(\alpha=0, 2, 4, 8\). In the game membership plots, each color indicates a different group of games in the most plausible model as obtained from Eqs. (8)–(11). The saturation of the color indicates how distributed a game is among groups, so that games with multiple memberships (typically at the border between groups) are paler (Fig. S4). In the distribution of the player entropies, players with a single strategy vector entropy \(H=0\) (red dashed line); players that mix two strategy vectors with equal weights have entropy \(H=\log_{3} 2 = 0.63\) (blue dashed line); and players that mix three strategy vectors with equal weights have entropy \(H=1\) (green dashed line). In the cooperation matrices p, each row corresponds to a group of players k, and each column to a group of games as indicated by the colors at the top. The height of player group k is proportional to the effective number of players in that group \(\sum_{i} \theta_{ik}\). The width of game group is proportional to the effective number of games in that group \(\sum_{g} \eta_{g\ell}\). Each element \(p_{k\ell}\) represents the probability that an individual in group k cooperates when playing a game in group , with dark red meaning always cooperate and dark blue always defect. The groups, entropies, and cooperation matrices correspond to one of the folds in the 5-fold cross-validation, but are very consistent across folds (see Fig. S6)

Back to article page