Numerical Probabilistic Approach to MFG

D. A. Gomes and H. Mitake. Existence for stationary mean-field games with congestion and quadratic Hamiltonians. Nonlinear Differential Equations and Applications NoDEA 22.6

1910

Earlier work this paper cites.

Y. V. Prokhorov (1956). Convergence of random processes and limit theorems in probability theory. Theory of Probability & Its Applications 1.2 (1956): 157-214

Original

1956

Earlier work this paper cites.

F. Delarue. On the Existence and Uniqueness of Solutions to FBSDEs in a Non-Degenerate Case. Stochastic Processes and Applications

2002

Earlier work this paper cites.

Bouchard, Bruno and Touzi, Nizar, Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their applications

2004

Earlier work this paper cites.

F. Delarue and S. Menozzi. A forward-backward stochastic algorithm for quasi-linear PDEs Ann. Appl. Probab

2006

Earlier work this paper cites.

M. Huang, P. E. Caines, and R. P. Malhamé. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Communications in Information and Systems

2006

Earlier work this paper cites.

J. M. Lasry, and P. L. Lions. Mean field games. Japanese journal of mathematics

2007

Earlier work this paper cites.

Y. Achdou and I. Capuzzo-Dolcetta. Mean field games: numerical methods SIAM J. Numer. Anal

2010

Earlier work this paper cites.

C. Harris, S. Howison, and R. Sircar. Games with exhaustible resources (2010). SIAM Journal on Applied Mathematics

2010

Earlier work this paper cites.

A. Lachapelle, J. Salomon and G. Turinici. Computation of mean field equilibria in economics, Mathematical Models and Methods in Applied Sciences

2010

Earlier work this paper cites.

A. Lachapelle, and M.T. Wolfram. On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transportation research part B: methodological

2011

Cited alongside, same era.

M. Nourian, P. E. Caines, and R. P. Malhamé. Synthesis of Cucker-Smale type flocking via mean field stochastic control theory: Nash equilibria. IEEE

2011

Cited alongside, same era.

M. Nourian, P. E. Caines, and R. P. Malhamé. Mean field analysis of controlled Cucker-Smale type flocking: Linear analysis and perturbation equations. IFAC Proceedings Volumes

2011

Cited alongside, same era.

O. Guéant. New numerical methods for mean field games with quadratic costs, Networks and Heterogeneous Media

2012

Cited alongside, same era.

Y. Achdou, F. Camilli and I. Capuzzo-Dolcetta. Mean field games: convergence of a finite difference method, SIAM J. Numer. Anal

2013

D. A. Gomes and J. Saúde. Mean field games models- a brief survey. Dynamic Games and Applications

2014

Later among the works it cites.

J.D. Benamou and G. Carlier, Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations, Journal of Optimization Theory and Applications

2015

Later among the works it cites.

Y. Achdou and M. Laurière. Mean field type control with congestion. Applied Mathematics & Optimization

2016

Later among the works it cites.

Y. Achdou and A. Porretta. Convergence of a Finite Difference Scheme to Weak Solutions of the System of Partial Differential Equations Arising in Mean Field Games, SIAM J. Numer. Anal

2016

Later among the works it cites.

P. Cardialaguet and C.A. Lehalle. Mean Field Game of Controls and An Application To Trade Crowding. arXiv:1610.09904[q-fin.TR] (2016)

Original