DocumentCode
1629602
Title
Time asymptotic behavior of the HJB equation associated with a class of mean-field games
Author
Arapostathis, Ari
Author_Institution
Electr. & Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA
fYear
2012
Firstpage
449
Lastpage
451
Abstract
We consider the HJB equation arising in mean-field games as in Lasry-Lions [1] but for a more general diffusion matrix, drift vector and running cost, with the data defined on ℝd. We examine a class of such problems for which there exists a stationary solution to the HJB, with an associated (unique) stationary probability distribution μ̅ ϵ P(ℝd). We show that as t → ∞ the law of the process associated to the solution of the mean-field HJB converges to μ and so does the value functions.
Keywords
game theory; statistical distributions; HJB equation; Lasry-Lions; diffusion matrix; drift vector; mean-field HJB; mean-field game; stationary probability distribution; stationary solution; time asymptotic behavior; value function; Conferences; Convergence; Educational institutions; Equations; Games; Markov processes; Process control;
fLanguage
English
Publisher
ieee
Conference_Titel
Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on
Conference_Location
Monticello, IL
Print_ISBN
978-1-4673-4537-8
Type
conf
DOI
10.1109/Allerton.2012.6483252
Filename
6483252
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