NDLI: Evolution of cooperation in a particular case of the infinitely repeated prisoner’s dilemma with three strategies

Content Provider	Springer Nature Link
Author	Neves, Armando G. M. Núñez Rodríguez, Irene
Copyright Year	2016
Abstract	We study a population of individuals playing the infinitely repeated prisoner’s dilemma under replicator dynamics. The population consists of three kinds of individuals adopting the following reactive strategies: ALLD (individuals which always defect), ATFT (almost tit-for-tat: individuals which almost always repeat the opponent’s last move) and G (generous individuals, which always cooperate when the opponent cooperated in the last move and have a positive probability q of cooperating when their opponent has defected). Our aim is studying in a mathematically rigorous fashion the dynamics of a simplified version for the computer experiment in Nowak and Sigmund (Nature 355:250–253, 1992) involving 100 reactive strategies. We see that as the generosity degree of the G individuals varies, equilibria (rest points) of the dynamics appear or disappear, and the dynamics changes accordingly. Not only we prove that the results of the experiment are true in our simplified version, but we also have complete control on the existence or non-existence of the equilbria for the dynamics for all possible values of the parameters, given that ATFT individuals are close enough to TFT. For most values of the parameters the dynamics can be completely determined.
Ending Page	1690
Page Count	26
Starting Page	1665
File Format	PDF
ISSN	03036812
e-ISSN	14321416
Journal	Journal of Mathematical Biology
Issue Number	6-7
Volume Number	73
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-04-19
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dynamical systems in biology Replicator dynamics Mathematical and Computational Biology Tit-for-tat Evolutionary games Nash equilibrium Applications of Mathematics Generous tit-fot-tat Problems related to evolution Evolutionary game theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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