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
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;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4673-4537-8
DOI :
10.1109/Allerton.2012.6483252
