Regularity for second order stationary mean-field games
By Edgard A. Pimentel, Vardan K. Voskanyan. 2015
47 citations recorded by the source corpus.
In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of long-time behavior of time-dependent mean-field games. Our argument is based on the interplay between the regularity of solutions of the Hamilton-Jacobi equation in terms of the solutions of the Fokker-Planck equation and vice-versa. Because we consider different classes of couplings, distinct techniques are used to obtain a priori estimates for the density. In the case of polynomial couplings, we recur to an iterative method. An integral method builds upon the properties of the logarithmic function in the setting of logarithmic nonlinearities. This work extends substantially previous results by allowing for more general classes of Hamiltonians and mean-field assumptions.
Subfields: Economics and Econometrics, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/39b576963615d41871b78952e357da04bfd5e860
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Citations in the corpus
- Stationary focusing mean-field games (2016, background): “The particular coupling −f(m) = logm, having the opposite monotonicity but lacking of boundedness from below, has been treated for example in [34, 16] (see also references therein).”