Cooperators can invade an incumbent population of defectors when one-shot prisoner's dilemmas occur multiple times within a generation. (December 2021) - Johnson, Tim; Smirnov, Oleg
Highlights: An analytic model reveals the effect of intra-generational time on cooperation in the one-shot prisoner's dilemma when no spatial dimension is present. When social interaction can occur at one out of multiple points in time, mutant cooperators can invade a well-mixed population of defectors under the replicator dynamics. Invasions lead to a nonequilbrium cycle of strategies in which cooperation consistently reemerges at alternating time points. Abstract: Researchers have identified numerous mechanisms that make cooperation in the prisoner's dilemma possible, yet recent research has proposed what ranks among the most basic of mechanisms: the presence of time. When organisms in spatial models can interact at multiple points in time within a generation, cooperation can evolve in a wider range of settings than in spatial models in which interaction occurs at a single moment. Here we further explore this mechanism via an analytic model that studies the effect of time on cooperation when no spatial dimension is present. The model shows that the mere presence of two or more points in time at which social interaction can occur creates an opportunity for mutant cooperators to invade a well-mixed population of defectors playing the one-shot prisoner's dilemma under the replicator dynamics. These invasions lead to a nonequilbrium cycling of strategies in which cooperation consistently reemerges at alternating time points.