Figure 1. Experimental paradigm and model-free analysis of Experiment 1. a, Single-trial illustration for social context (top panel) and nonsocial context (bottom panel). b, Partner’s cooperation probability throughout the PDG. c-d, Behavioral analysis results of Experiment 1. c, The x-axis represents the independent variables, and the y-axis represents the effect sizes (beta values from GLMM) of the independent variables in explaining participants' cooperation behavior. d, The interaction between scenario and probability (left panel) and the difference in participants' cooperation probabilities between partners’ high and low probability conditions (high probability - low probability) for both social and nonsocial contexts (right panel). The height of the bars represents the mean value ± SE. Each line crossing the bars in the right figure represents data for an individual participant. ***p < 0.001, ns. p > 0.05.

Figure 2. Model-based analysis of Experiment 1. a, Model comparison. The x-axis represents the different models, and the y-axis represents the Bayesian Information Criterion (BIC) values, calculated as BIC = k·ln(n) − 2·ln(L). Under both the social (yellow bars) and nonsocial (blue bars) conditions, the participants' behavior was best explained by Model 6. b, Model recovery analysis. Each model was used to generate 100 synthetic datasets, for each of which model fitting and comparison were performed. Each column represents one generative model. Each row represents one fitting model. The color in each cell indicates the probability that the synthetic datasets from the generative model in the column are best fit by the fitting model in the row, with darker colors indicating higher probability. c, The behavioral prediction from the best-fitting model. The x-axis represents the trial number, and the y-axis represents the mean cooperation probability of the participants. The blue line represents the participants' actual choices, the black line represents the predictions of the best-fitting model, and the shaded area represents the 95% confidence interval of the predicted cooperation rate from the best-fitting model. d-e, Analysis of the social reward (ω) and expectation (p) parameters from the best-fitting model. The interaction between scenario and probability (left panel) and the difference in participants' cooperation probabilities between partners’ high and low probability conditions (high probability - low probability) for both social and nonsocial contexts (right panel). The height of the bars represents the mean value ± SE. Each line crossing the bars in the right figure represents data for an individual participant. ***p < 0.001.

Figure 3. Model-free and model-based analysis results of Experiment 2. a, Partner’s cooperation probability throughout the PDG in Experiment 2. b, Model comparison. c-d, Behavioral analysis results of Experiment 2. c, The x-axis represents the independent variables, and the y-axis represents the effect sizes (beta values from GLMM) of the independent variables in explaining participants’ cooperation behavior. d, The interaction between scenario and probability. e-f, Analysis of the social reward (ω) and expectation (p) parameters from the best-fitting model. The height of the bars represents the mean value ± SE. ***p < 0.001.