Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
dc.contributor.author | Burger, Martin | |
dc.contributor.author | Lorz, Alexander | |
dc.contributor.author | Wolfram, Marie Therese | |
dc.date.accessioned | 2017-02-15T08:32:14Z | |
dc.date.available | 2017-02-15T08:32:14Z | |
dc.date.issued | 2016-11-18 | |
dc.identifier.citation | Wolfram 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.issn | 1937-5093 | |
dc.identifier.doi | 10.3934/krm.2017005 | |
dc.identifier.uri | http://hdl.handle.net/10754/622883 | |
dc.description.abstract | In 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.sponsorship | MTW 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.publisher | American Institute of Mathematical Sciences (AIMS) | |
dc.relation.url | http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=13315 | |
dc.subject | Boltzmann-type equations | |
dc.subject | Hamilton-Jacobi equations | |
dc.subject | Mean-field games | |
dc.subject | Travelling wave solutions | |
dc.title | Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth | |
dc.type | Article | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.identifier.journal | Kinetic & Related Models | |
dc.contributor.institution | Institute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, Münster, 48149, Germany | |
dc.contributor.institution | Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, F-75005, France | |
dc.contributor.institution | CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, F-75005, France | |
dc.contributor.institution | INRIA-Paris-Rocquencourt, EPC MAMBA, Domaine de Voluceau, BP105, Le Chesnay Cedex, 78153, France | |
dc.contributor.institution | University of Warwick, Coventry, CV4 7AL, United Kingdom | |
dc.contributor.institution | RICAM, Austrian Academy of Sciences, Altenbergerstr. 69, Linz, 4040, Austria | |
dc.identifier.arxivid | 1602.01423 | |
kaust.person | Lorz, Alexander | |
dc.date.published-online | 2016-11-18 | |
dc.date.published-print | 2016-11 |
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