Abstract: People usually exhibit conditional cooperative behavior during cooperation; that is, they cooperate only when they expect others will cooperate as well. The cognitive computations and the dynamic processes underlying such conditional cooperation in repeated interactions remain underexplored. To this end, this study investigates the cognitive mechanisms behind conditional cooperation, focusing on two hidden mental variables: positive expectation (participants' expected cooperation willingness of the partner) and the perception of social reward (additional reward derived from reciprocity).
Using a repeated aversion of Prisoner's Dilemma Game (PDG), we conducted two experiments (n = 134 in Experiment 1 and n = 104 in Experiment 2) in this study. Nonsocial context (playing PDG with a computer program) was created to test if the effects are specific to social context (playing PDG with a supposed human partner). By manipulating partners' cooperation probabilities and response variability, we explored how positive expectation and social reward evolve during cooperation and to affect participants' behavioral outputs. We systematically developed six models to model participants' decision process during PDG. These models range from baseline model with random choice assumption (Model 1) to more complex formulations incorporating reward-based learning (Model 2), rational choice theory (Model 3), social reward (Model 4), and the integration of different learning rules (Models 5 to 6).
The results of two experiments consistently demonstrated that participants dynastically adjust their cooperation decisions in response to their partners' behaviors. After separating the effects that may be brought by the partner's cooperation probability from those of response vocality, we found that participants' cooperation increases with their partner's increased cooperative behaviors, rather than with the partner's response volatility, an effect specific to social context. Model comparisons showed that participants' behaviors in both social and nonsocial contexts were best described by a model assuming social rewards and incorporating a learning algorithm that includes both first-order beliefs (based solely on others' past behavior) and second-order beliefs (considering both others' past behavior and the influence of their own behavior on others) to update their expectations of their partners' cooperation. The results indicated that increasing conditional cooperation is driven by both participants' positive expectation and social reward, effects that were specific to a social context.
This study elucidated the cognitive computational dynamics of conditional cooperation, highlighted the roles of positive expectation and social reward, and showed that people applied a complex model with both first-order and second-order beliefs to update their expectations of their partner's willingness to cooperate. These contributions underscore the importance of understanding the mental processes that encourage mutual cooperation. Future studies might explore the neural correlates of these mechanisms or apply these insights to more complex scenarios, bridging the gap between laboratory research findings and real-world collaboration.

Key words: conditional cooperation, social reward, positive expectation, cognitive computational modeling, belief update