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dc.contributor.authorBurger, Martin
dc.contributor.authorLorz, Alexander
dc.contributor.authorWolfram, Marie Therese
dc.date.accessioned2017-02-15T08:32:14Z
dc.date.available2017-02-15T08:32:14Z
dc.date.issued2016-11-18
dc.identifier.citationWolfram M-T, Lorz A, Burger M (2016) Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth. Kinetic and Related Models 10: 117–140. Available: http://dx.doi.org/10.3934/krm.2017005.
dc.identifier.issn1937-5093
dc.identifier.doi10.3934/krm.2017005
dc.identifier.urihttp://hdl.handle.net/10754/622883
dc.description.abstractIn this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We prove existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.
dc.description.sponsorshipMTW acknowledges financial support from the Austrian Academy of Sciences OAW via the New Frontiers Group NST-001. This research was funded in part by the French ANR blanche project Kibord: ANR-13-BS01- 0004. The authors thank Benjamin Moll for the helpful discussions and comments while preparing the manuscript.
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.urlhttp://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=13315
dc.subjectBoltzmann-type equations
dc.subjectHamilton-Jacobi equations
dc.subjectMean-field games
dc.subjectTravelling wave solutions
dc.titleBalanced growth path solutions of a Boltzmann mean field game model for knowledge growth
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalKinetic and Related Models
dc.contributor.institutionInstitute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, Münster, 48149, Germany
dc.contributor.institutionSorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, F-75005, France
dc.contributor.institutionCNRS, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, F-75005, France
dc.contributor.institutionINRIA-Paris-Rocquencourt, EPC MAMBA, Domaine de Voluceau, BP105, Le Chesnay Cedex, 78153, France
dc.contributor.institutionUniversity of Warwick, Coventry, CV4 7AL, United Kingdom
dc.contributor.institutionRICAM, Austrian Academy of Sciences, Altenbergerstr. 69, Linz, 4040, Austria
dc.identifier.arxividarXiv:1602.01423
kaust.personLorz, Alexander
dc.date.published-online2016-11-18
dc.date.published-print2016-11


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