  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.
