Presentation Title
P-34 The Existence and Uniqueness of a Nash Equilibrium in Mean Field Game Theory
Presenter Status
Undergraduate, Andrews University Department of Mathematics
Second Presenter Status
Undergraduate, Duke University Department of Mathematics
Third Presenter Status
Professor, University of California, Los Angeles Department of Mathematics
Preferred Session
Poster Session
Location
Buller Hall Hallways
Start Date
21-10-2022 2:00 PM
End Date
21-10-2022 3:00 PM
Presentation Abstract
In recent and past works, convexity is usually assumed on each individual part of the action functional in order to demonstrate the existence and uniqueness of a Nash equilibrium on some interval [0,T] (this meant that each hessian was assumed to be nonnegative). Particularly, a certain assumption was imposed in order to quantify the smallness of T. The contribution of this project is to expand on this with the key insight being that one does not need the convexity of each part of the action, but rather just an appropriate combination of them, which will essentially ``compensate'' for the other two terms to yield convexity in the action.
This is meaningful in both the pure and applied settings as it generalizes the existence and uniqueness of a Nash equilibrium slightly more, but maybe more importantly matches real-world application slightly closer, as in reality there are many settings in which not each part of the action have convexity. Thus, it is more accurate for modern application of Mean Field Game Theory.
P-34 The Existence and Uniqueness of a Nash Equilibrium in Mean Field Game Theory
Buller Hall Hallways
In recent and past works, convexity is usually assumed on each individual part of the action functional in order to demonstrate the existence and uniqueness of a Nash equilibrium on some interval [0,T] (this meant that each hessian was assumed to be nonnegative). Particularly, a certain assumption was imposed in order to quantify the smallness of T. The contribution of this project is to expand on this with the key insight being that one does not need the convexity of each part of the action, but rather just an appropriate combination of them, which will essentially ``compensate'' for the other two terms to yield convexity in the action.
This is meaningful in both the pure and applied settings as it generalizes the existence and uniqueness of a Nash equilibrium slightly more, but maybe more importantly matches real-world application slightly closer, as in reality there are many settings in which not each part of the action have convexity. Thus, it is more accurate for modern application of Mean Field Game Theory.
Acknowledgments
University of California, Los Angeles (UCLA), David Harold Blackwell Summer Research Institute 2022 (DHBSRI)