title: Socio-economic applications of finite state mean field games.
abstract: In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
authors.affiliation: Computer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia diogo.gomes@kaust.edu.sa.
authors.forename: Diogo
authors.initials: D
authors.lastname: Gomes
authors.affiliation: Computer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia.
authors.forename: Roberto M
authors.initials: RM
authors.lastname: Velho
authors.affiliation: Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040 Linz, Austria.
authors.forename: Marie-Therese
authors.initials: MT
authors.lastname: Wolfram
keywords: finite state space; mean field games; numerical methods; socio-economic applications