Random topologies and the emergence of cooperation: the role of short-cuts

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We study in detail the role of short-cuts in promoting the emergence of cooperation in a network of agents playing the Prisoner’s Dilemma game (PDG). We introduce a model whose topology interpolates between the onedimensional Euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p of adding a link between two nodes not already connected in the Euclidean configuration). We show that there is a region of values of p in which cooperation is greatly enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p → 1− cooperation is totally suppressed. We present analytical arguments that provide a very plausible interpretation of the simulation results, thus unveiling the mechanism by which short-cuts contribute to promoting (or suppressing) cooperation.
IOPscience
Journal of Statistical Mechanics: Theory and Experiment, abril 2011, P04019 (15 pgs.)
DV was supported in part by a postdoctoral contract from Universidad Carlos III de Madrid. AS was supported in part by grants MOSAICO and Complexity-NET RESINEE (Ministerio de Ciencia e Innovaci´on, Spain) and MODELICO-CM (Comunidad de Madrid, Spain). JG-G was supported by the MICINN through the Ram´on y Cajal programme and grants FIS2008-01240 and MTM2009-13838.

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Published 01 April 2011
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Random topologies and the emergenceof cooperation: the role of short-cutsD Vilone1,AS´anchez1,2,3andJG´omez-Garde˜nes3,41Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento deMatem´aticas,UniversidadCarlosIIIdeMadrid,28911Legan´es,Madrid,Spain2InstitutodeCienciasMatem´aticasCSIC-UAM-UC3M-UCM,28049 Cantoblanco, Madrid, Spain3InstitutodeBiocomputaci´onyFı´sicadeSistemasComplejos,UniversidaddeZaragoza, Campus R´ıo Ebro, 50018 Zaragoza, Spain4Departamento de Matem´atica Aplicada, Universidad Rey Juan Carlos,28933M´ostoles,Madrid,SpainE-mail:daniele.vilone@gmail.com,anxo@math.uc3m.esandgardenes@gmail.com
Abstract.We study in detail the role of short-cuts in promoting the emergenceof cooperation in a network of agents playing the Prisoner’s Dilemma game(PDG). We introduce a model whose topology interpolates between the one-dimensional Euclidean lattice (a ring) and the complete graph by changing thevalue of one parameter (the probabilitypof adding a link between two nodesnot already connected in the Euclidean configuration). We show that thereis a region of values ofpin which cooperation is greatly enhanced, whilst forsmaller values ofponly a few cooperators are present in the final state, and forp1cooperation is totally suppressed. We present analytical arguments thatprovide a very plausible interpretation of the simulation results, thus unveilingthe mechanism by which short-cuts contribute to promoting (or suppressing)cooperation.Keywords:game-theory (theory), models for evolution (theory), applications togame theory and mathematical economics, interacting agent modelsArXiv ePrint:1010.3547