Uncertainty quantification for mean field games in social interactions

Handle URI:
http://hdl.handle.net/10754/624870
Title:
Uncertainty quantification for mean field games in social interactions
Authors:
Dia, Ben Mansour
Abstract:
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
9-Jan-2016
Type:
Presentation
Appears in Collections:
Presentations; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorDia, Ben Mansouren
dc.date.accessioned2017-06-08T06:32:30Z-
dc.date.available2017-06-08T06:32:30Z-
dc.date.issued2016-01-09-
dc.identifier.urihttp://hdl.handle.net/10754/624870-
dc.description.abstractWe present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.en
dc.titleUncertainty quantification for mean field games in social interactionsen
dc.typePresentationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
kaust.authorDia, Ben Mansouren
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