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Generosity pays in the presence of direct reciprocity: a comprehensive study of 2x2 repeated games

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Interdisciplinar de Sistemas Complejos (GISC)es
dc.contributor.authorMartínez-Vaquero, Luis A.
dc.contributor.authorCuesta, José A.
dc.contributor.authorSánchez, Angel
dc.date.accessioned2014-06-11T12:36:20Z
dc.date.available2014-06-11T12:36:20Z
dc.date.issued2012-04-18
dc.description.abstractBy applying a technique previously developed to study ecosystem assembly [Capita´n et al., Phys. Rev. Lett. 103, 168101 (2009)] we study the evolutionary stable strategies of iterated 2|2 games. We focus on memory-one strategies, whose probability to play a given action depends on the actions of both players in the previous time step. We find the asymptotically stable populations resulting from all possible invasions of any known stable population. The results of this invasion process are interpreted as transitions between different populations that occur with a certain probability. Thus the whole process can be described as a Markov chain whose states are the different stable populations. With this approach we are able to study the whole space of symmetric 2|2 games, characterizing the most probable results of evolution for the different classes of games. Our analysis includes quasi-stationary mixed equilibria that are relevant as very long-lived metastable states and is compared to the predictions of a fixation probability analysis. We confirm earlier results on the success of the Pavlov strategy in a wide range of parameters for the iterated Prisoner’s Dilemma, but find that as the temptation to defect grows there are many other possible successful strategies. Other regions of the diagram reflect the equilibria structure of the underlying one-shot game, albeit often some non-expected strategies arise as well. We thus provide a thorough analysis of iterated 2|2 games from which we are able to extract some general conclusions. Our most relevant finding is that a great deal of the payoff parameter range can still be understood by focusing on win-stay, lose-shift strategies, and that very ambitious ones, aspiring to obtaining always a high payoff, are never evolutionary stableen
dc.description.sponsorshipThis work was supported in part by Ministerio de Ciencia e Innovación, Spain (http://www.micinn.es) through grants MOSAICO and PRODIEVO, by European Research Area Complexity-Net (http://www.complexitynet.eu) though grant RESINEE, and by Comunidad de Madrid, Spain (http://www.madrid.org) through grant MODELICO. Luis A. Martínez-Vaquero was supported by a postdoctoral fellowship from Alianza 4 Universidades (http://www.alliance4universities. eu). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.en
dc.format.extent12
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationPLoS ONE, 7(4), e35135, pp. 1-12en
dc.identifier.doihttps://doi.org/10.1371/journal.pone.0035135
dc.identifier.issn1932-6203
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue4 (e35135)
dc.identifier.publicationlastpage12
dc.identifier.publicationtitlePloS Oneen
dc.identifier.publicationvolume7
dc.identifier.urihttps://hdl.handle.net/10016/18984
dc.identifier.uxxiAR/0000010124
dc.language.isoeng
dc.publisherPLoS
dc.relation.projectIDComunidad de Madrid. S2009/ESP-1691/MODELICOes
dc.relation.projectIDGobierno de España. FIS2011-22449/PRODIEVO
dc.relation.projectIDGobierno de España. FIS2006-01485/MOSAICO
dc.rights© 2012 Martinez-Vaquero et al.
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.ecienciaMatemáticases
dc.subject.otherTit-for-taten
dc.subject.otherPrisoner's dilemmaen
dc.subject.otherGenetical evolutionen
dc.subject.otherFinite automataen
dc.subject.otherLose-shiften
dc.subject.otherWin-stayen
dc.subject.otherCooperationen
dc.subject.otherRulesen
dc.subject.otherChaosen
dc.titleGenerosity pays in the presence of direct reciprocity: a comprehensive study of 2x2 repeated gamesen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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