Stochastic strategies in the prisoner's dilemma
type: Item
instance of: scholarly article
title: Stochastic strategies in the prisoner's dilemma
zbMATH Open document ID: 0726.92015
DOI: 10.1016/0040-5809(90)90005-G
published in: Theoretical Population Biology
publication date: 1990-01-01T00:00:00Z
review text: In the repeated prisoner's dilemma, the (deterministic) Tit-for-Tat strategy has been known to be highly successful. Motivated by the observation that in biological applications there is always some uncertainty or noise, the author argues that it is more appropriate to consider stochastic (mixed) strategies. He gives a complete analysis of all strategies where the probability to cooperate depends only on the opponent's previous move for the infinitely repeated prisoner's dilemma. All Nash solutions are characterized. Specifically (ignoring the initial move which will not matter in the long run if the transition matrix generated by the strategies is mixing), a strategy is given by p and q, where p resp. q is the probability to cooperate given that the other player's previous choice was ``cooperate'' resp. ``defect''. It is shown that \(p=1\) (never defect after cooperation) is a necessary condition for stability against invasion by selection pressure. There exists a region of possible strategies where cooperation increases due to mutation-selection forces. There exists also a region where less cooperative strategies can invade.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 91A40
zbMATH DE Number: 4200032
zbMATH Keywords: stochastic strategies
zbMATH Keywords: Nash solutions
zbMATH Keywords: evolutionary stability
zbMATH Keywords: Tit-for- Tat strategy
zbMATH Keywords: infinitely repeated prisoner's dilemma
zbMATH Keywords: cooperation
zbMATH Keywords: stability against invasion
zbMATH Keywords: selection pressure
zbMATH Keywords: mutation-selection forces
author: Martin A. Nowak
reviewed by: Manfred Nermuth
MaRDI profile type: Publication
cites work: Q3956774
cites work: The Evolution of Cooperation
cites work: Q3040961
cites work: Game-dynamical aspects of the prisoner's dilemma
full work available at URL: 0040-5809(90)90005-g
OpenAlex ID: W2027398667
description: scientific article; zbMATH DE number 4200032