Strategy dependent time delays shape cooperation in the spatial prisoner’s dilemma game

Abstract

Understanding how temporal aspects of decision-making influence cooperation in structured populations is crucial for explaining the emergence of cooperative behavior in nature and society. While spatial reciprocity has long been known to support cooperation by allowing cooperators to form protective clusters, the role of time delays, particularly those dependent on strategy choice, remains underexplored. Here, we investigate the effects of strategy-dependent time delays on cooperation dynamics in the weak Prisoner’s Dilemma game on square lattices. Using Monte Carlo simulations, we show that time delays can profoundly alter cooperation levels and spatial patterns. Our results reveal that asymmetries in delays can induce transitions between full cooperation, coexistence, and full defection. Also we show that strategy-dependent delays primarily alter the clustering dynamics of cooperators, which in turn drives the changes in overall cooperation behavior. We further show that the type of Prisoner’s Dilemma (weak or standard) influences only the quantitative level of cooperation, while the qualitative effect of delays remains unchanged.