On the coexistence of cooperators, defectors and conditional cooperators in the multiplayer iterated Prisoner's dilemma

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dc.contributor.author Grujić, Jelena
dc.contributor.author Cuesta, José A.
dc.contributor.author Sánchez, Angel
dc.date.accessioned 2015-03-05T12:10:41Z
dc.date.available 2015-03-05T12:10:41Z
dc.date.issued 2012-05-07
dc.identifier.bibliographicCitation Journal of Theoretical Biology, (7 May 2012), v.300, pp.299-308
dc.identifier.issn 0022-5193
dc.identifier.uri http://hdl.handle.net/10016/20179
dc.description.abstract Recent experimental evidence [Grujić Fosco, Araujo, Cuesta, Sánchez, 2010. Social experiments in the mesoscale: humans playing a spatial Prisoner's dilemma. PLoS ONE 5, e13749] on the spatial Prisoner's Dilemma suggests that players choosing to cooperate or not on the basis of their previous action and the actions of their neighbors coexist with steady defectors and cooperators. We here study the coexistence of these three strategies in the multiplayer iterated Prisoner's Dilemma by means of the replicator dynamics. We consider groups with n=2, 3, 4 and 5 players and compute the payoffs to every type of player as the limit of a Markov chain where the transition probabilities between actions are found from the corresponding strategies. We show that for group sizes up to n=4 there exists an interior point in which the three strategies coexist, the corresponding basin of attraction decreasing with increasing number of players, whereas we have not been able to locate such a point for n =5. We analytically show that in the limit n→∞n→∞ no interior points can arise. We conclude by discussing the implications of this theoretical approach on the behavior observed in experiments.
dc.description.sponsorship This work was supported in part by MICINN (Spain) through grants PRODIEVO and MOSAICO, by ERA-NET Complexity-Net RESINEE, and by Comunidad de Madrid (Spain) through grant MODELICO-CM).
dc.format.extent 10
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2012 Elsevier Ltd.
dc.subject.other Evolution
dc.subject.other Prisoner's dilemma
dc.subject.other Conditional cooperation
dc.subject.other Game theory
dc.subject.other Replicator dynamics
dc.title On the coexistence of cooperators, defectors and conditional cooperators in the multiplayer iterated Prisoner's dilemma
dc.type article
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jtbi.2012.02.003
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.jtbi.2012.02.003
dc.rights.accessRights openAccess
dc.relation.projectID Comunidad de Madrid. S2009/ESP-1691/MODELICO
dc.relation.projectID Gobierno de España. FIS2011-22449/PRODIEVO
dc.relation.projectID Gobierno de España. FIS2006-01485/MOSAICO
dc.type.version submittedVersion
dc.identifier.publicationfirstpage 299
dc.identifier.publicationlastpage 308
dc.identifier.publicationtitle Journal of Theoretical Biology
dc.identifier.publicationvolume 300
dc.identifier.uxxi AR/0000009872
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