Prime numbers and the evolution of cooperation, I: A prisoner's dilemma model that identifies prime numbers via invasions of cooperators. (December 2022)

• Record Type: Journal Article
• Authors: Johnson, Tim
• Is Part Of: Chaos, solitons & fractals. Volume 9(2022)
• Publication Date: 2022-12
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Solitons; Fractals; Chaotic behavior in systems; Periodicals; Electronic journals; 003.7
• DOI: 10.1016/j.csfx.2022.100081
• Languages: English
• ISSNs: 2590-0544

Abstract

Highlights: An analytic evolutionary game theory model involving the prisoner's dilemma is shown to identify the prime numbers. The model confirms a longstanding hypothesis positing a connection between prime numbers and the cross-disciplinary puzzle of how cooperation evolved. The model provides a theoretical foundation for future research into strategies for cooperation and free-riding when social interaction occurs across discrete time points with varying social partners. Abstract: The development of methods to identify prime numbers spans centuries and includes models of physical and biological systems that spot primes. This paper adds to the latter research genre by reporting a prisoner's dilemma model that identifies prime numbers greater than 2. Albeit containing unconventional features and arguable assumptions, the model nonetheless confirms a previously hypothesized connection between prime numbers and the cross-disciplinary puzzle of how cooperation evolved. In a companion paper (part II), the features and assumptions of the analytic model reported here are explored in a finite-population, computational model.