Emergent cooperative decision-making in triadic Prisoner's Dilemmas: Effects of incentives and information

While pairwise cooperation has been extensively studied through the Prisoner's Dilemma (PD), our understanding of how cooperation emerges in small groups remains limited. We extend the classic dyadic PD framework to a triadic framework, examining two sets of PD games per individual and how individual strategies and relationships aggregate to group cooperation. Through two experiments (N=519), we investigate: (1) how structural incentives shape cooperation by varying the K-index (0.4/0.8), a theoretical value that predicts greater cooperation for higher K values, and (2) how different degrees of information about mutual interdependence affect group behavior. We find that, under minimal information conditions, a higher K-index promotes sustained cooperation in the triadic setting, in alignment with the theoretical definition of the K-index. However, while experiential information (observing others' actions/outcomes) enhances cooperation, descriptive information (complete payoff matrices) paradoxically reduces cooperation. Analysis of triadic interactions reveals that selective cooperation by a third player in the group can stabilize cooperative dyadic relationships and destabilize defective dyadic relationships. These findings provide insights for designing cooperative systems, particularly in contexts where organizations must balance information sharing benefits against strategic risks.