A Finite Dimensional Approximation of a Density Dependent Mean Field Game

dc.contributor.advisorGraber, Jameson
dc.contributor.authorZimmerman, Brady
dc.contributor.departmentUniversity Scholars.
dc.contributor.otherBaylor University.en
dc.contributor.schoolsHonors College - Honors Program
dc.date.accessioned2024-06-05T18:18:19Z
dc.date.available2024-06-05T18:18:19Z
dc.date.copyright2024
dc.date.issued2024
dc.description.abstractThe goal of this thesis is to establish the existence and uniqueness of a Nash equilibrium of a density dependent mean field game and approximate the solution with numerical methods. We first briefly introduce both mean field game theory and measure theory. Next, we define a game in which the final cost is the density of the equilibrium measure. Then we prove a unique solution exists by using the Browder-Minty Theorem. To conclude, we will show how Newton’s method can be used to approximate a solution and look at some specific examples of this approximation in action.
dc.identifier.urihttps://hdl.handle.net/2104/12761
dc.language.isoen_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
dc.rights.accessrightsWorldwide access
dc.subjectMathematics
dc.titleA Finite Dimensional Approximation of a Density Dependent Mean Field Game
dc.typeThesisen

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