Asymptotics for mean field games of market competition

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dc.contributor.advisorGraber, Jameson
dc.contributor.authorLaurel, Marcus
dc.contributor.departmentMathematics.en_US
dc.contributor.otherBaylor University.en_US
dc.contributor.schoolsHonors College.en_US
dc.date.accessioned2018-12-04T17:32:26Z
dc.date.available2018-12-04T17:32:26Z
dc.date.copyright2018
dc.date.issued2018-12-04
dc.description.abstractThe goal of this thesis is to analyze the limiting behavior of solutions to a system of mean field games developed by Chan and Sircar to model Bertrand and Cournot competition. We first provide a basic introduction to control theory, game theory, and ultimately mean field game theory. With these preliminaries out of the way, we then introduce the model first proposed by Chan and Sircar, namely a coupled system of two nonlinear partial differential equations. This model contains a parameter ε that measures the degree of interaction between players; we are interested in the regime ε goes to 0. We then prove a collection of theorems which give estimates on the limiting behavior of solutions as ε goes to 0 and ultimately obtain recursive growth bounds of polynomial approximations to solutions. Finally, we state some open questions for further research.en_US
dc.identifier.urihttps://hdl.handle.net/2104/10470
dc.language.isoen_USen_US
dc.rightsBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.en_US
dc.rights.accessrightsWorldwide accessen_US
dc.titleAsymptotics for mean field games of market competitionen_US
dc.typeThesisen_US

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