Temporal Interaction and its Role in the Evolution of Cooperation

This research investigates the impact of dynamic interactions with time-varying topologies on the evolution of cooperative behaviours in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction frequency and synchronicity on cooperation remains underexplored. Addressing this gap, our work introduces two temporal interaction mechanisms to model the stochastic or periodic participation of individuals in these games, acknowledging real-life variances due to exogenous temporal factors and geographical time differences. We consider that the interaction state significantly influences both game payoff calculations and the strategy updating process, offering new insights into the emergence and sustainability of cooperation. Our results indicate that maximum game participation frequency is suboptimal under a stochastic interaction mechanism. Instead, an intermediate region of activation probability yields the highest cooperation level, especially under strong dilemma conditions. This suggests that a balance between inactivity security and interaction frequency is crucial. Furthermore, local synchronization of interactions within specific areas is shown to be beneficial, as time differences hinder the spread of cross-structures but promote the formation of dense cooperative clusters with smoother boundaries. Our findings provide an intuitive understanding of node-based temporality and probabilistic interactions, contributing to the broader discourse on resolving social dilemmas.