Purely competitive evolutionary dynamics for games

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dc.contributor.authorVeller, Carl
dc.contributor.authorRajpaul, Vinesh
dc.date.accessioned2021-10-08T07:11:35Z
dc.date.available2021-10-08T07:11:35Z
dc.date.issued2012
dc.description.abstractWe introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.
dc.identifier.apacitationVeller, C., & Rajpaul, V. (2012). Purely competitive evolutionary dynamics for games. <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i>, 86(4), 174 - 177. http://hdl.handle.net/11427/34647en_ZA
dc.identifier.chicagocitationVeller, Carl, and Vinesh Rajpaul "Purely competitive evolutionary dynamics for games." <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics</i> 86, 4. (2012): 174 - 177. http://hdl.handle.net/11427/34647en_ZA
dc.identifier.citationVeller, C. & Rajpaul, V. 2012. Purely competitive evolutionary dynamics for games. <i>Physical Review E - Statistical, Nonlinear, and Soft Matter Physics.</i> 86(4):174 - 177. http://hdl.handle.net/11427/34647en_ZA
dc.identifier.issn1539-3755
dc.identifier.issn1550-2376
dc.identifier.ris TY - Journal Article AU - Veller, Carl AU - Rajpaul, Vinesh AB - We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable. DA - 2012 DB - OpenUCT DP - University of Cape Town IS - 4 J1 - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics LK - https://open.uct.ac.za PY - 2012 SM - 1539-3755 SM - 1550-2376 T1 - Purely competitive evolutionary dynamics for games TI - Purely competitive evolutionary dynamics for games UR - http://hdl.handle.net/11427/34647 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/34647
dc.identifier.vancouvercitationVeller C, Rajpaul V. Purely competitive evolutionary dynamics for games. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2012;86(4):174 - 177. http://hdl.handle.net/11427/34647.en_ZA
dc.language.isoeng
dc.publisher.departmentDepartment of Astronomy
dc.publisher.facultyFaculty of Science
dc.sourcePhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
dc.source.journalissue4
dc.source.journalvolume86
dc.source.pagination174 - 177
dc.source.urihttps://dx.doi.org/10.1103/PhysRevE.86.041907
dc.subject.otherAlgorithms
dc.subject.otherAnimals
dc.subject.otherBiological Evolution
dc.subject.otherBiophysics
dc.subject.otherCompetitive Behavior
dc.subject.otherComputer Simulation
dc.subject.otherGame Theory
dc.subject.otherModels, Biological
dc.subject.otherModels, Genetic
dc.subject.otherModels, Statistical
dc.subject.otherModels, Theoretical
dc.subject.otherMutation
dc.subject.otherPopulation Dynamics
dc.subject.otherProbability
dc.subject.otherSelection, Genetic
dc.subject.otherSexual Behavior, Animal
dc.titlePurely competitive evolutionary dynamics for games
dc.typeJournal Article
uct.type.publicationResearch
uct.type.resourceJournal Article
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