On the Planning Problem for the Mean Field Games System

Alessio Porretta ()

Dynamic Games and Applications, 2014, vol. 4, issue 2, 256 pages

Abstract: We consider the planning problem for a class of mean field games, consisting in a coupled system of a Hamilton–Jacobi–Bellman equation for the value function u and a Fokker–Planck equation for the density m of the players, whereas one wishes to drive the density of players from the given initial configuration to a target one at time T through the optimal decisions of the agents. Assuming that the coupling F(x,m) in the cost criterion is monotone with respect to m, and that the Hamiltonian has some growth bounded below and above by quadratic functions, we prove the existence of a weak solution to the system with prescribed initial and terminal conditions m 0 , m 1 (positive and smooth) for the density m. This is also a special case of an exact controllability result for the Fokker–Planck equation through some optimal transport field. Copyright Springer Science+Business Media New York 2014

Keywords: Mean field games; Planning problem; Optimal transport problem; Exact controllability (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s13235-013-0080-0 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dyngam:v:4:y:2014:i:2:p:231-256

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-013-0080-0

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().