2015/09/03 by Irene Núñez Rodríguez, A. Neves, Rodríguez, Irene Núñez +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Social Sciences · #37N25 #91A22 #91C99 #92D15 #Biological Physics (physics.bio-ph) #Classical Analysis and ODEs (math.CA) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Opinion Dynamics and Social Influence #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1509.01225
openalex publication_date 2015/09/03 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
We will study a population of individuals playing the infinitely repeated\nPrisoner's Dilemma under replicator dynamics. The population consists of three\nkinds of individuals using the following reactive strategies: ALLD (individuals\nwhich always defect), ATFT (almost tit-for-tat: individuals which almost always\nrepeat the opponent's last move) and G (generous individuals, which always\ncooperate when the opponent cooperated in the last move and have a positive\nprobability q of cooperating when they are defected). Our aim is studying in\na mathematically rigorous fashion the dynamics of a simplified version for the\ncomputer experiment in [Nowak, Sigmund, Nature, 355, pp. 250--53, 1992]\ninvolving 100 reactive strategies. We will see that as the generosity degree of\nthe G individuals varies, equilibria (rest points) of the dynamics appear or\ndisappear, and the dynamics changes accordingly. Not only we will prove that\nthe results of the experiment are true in our simplified version, but we will\nhave complete control on the existence or non-existence of the equilbria for\nthe dynamics for all possible values of the parameters, given that ATFT\nindividuals are close enough to TFT. For most values of the parameters the\ndynamics will be completely determined.\n