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AbstractIn 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.
CitationGomes D, Velho RM, Wolfram M-T (2014) Socio-economic applications of finite state mean field games. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372: 20130405–20130405. Available: http://dx.doi.org/10.1098/rsta.2013.0405.
SponsorsD. G. was partially supported by KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering and CAMGSD-LARSys (FCT-Portugal), PTDC/MAT-CAL/0749/2012 (FCT-Portugal). R. M. V. was partially supported by CNPq-Brazil through a PhD scholarship 'Programme Science without Borders and KAUST' Saudi Arabia. M.-T.W. acknowledges support from the Austrian Academy of Sciences OAW via the New Frontiers Project NST-001.
PublisherThe Royal Society
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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