Prime numbers and the evolution of cooperation, II: Advantages to cooperators using prime-number period lengths in a finite population constrained to prisoner's dilemma strategies that alternate between periods of activity and inactivity

Abstract

• The paper reports a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. • Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. • Simulation results dovetail with the findings of a recent analytic model that confirmed a longstanding, hypothesized link between the prime numbers and the evolution of cooperation. • The findings suggest that schedules with prime-number period lengths constitute a new mechanism for the evolution of cooperation. • Viewed in concert with the findings of past-predator prey models, the results raise the possibility that cyclical behavior with prime-number period lengths might serve as an adaptive solution to a range of challenges that lifeforms face. This paper presents a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. Evolutionary selection acts on agents’ behavioral dispositions to cooperate/defect and the schedules that determine when agents periodically implement that behavior. Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. These findings reinforce recent analytic findings that indicate a connection between the evolution of cooperation and the prime numbers, plus they offer new empirical predictions about the timing of social behavior.