From infinity to one: The reduction of some mean field games to a global control problem
Optimization and Control
2011-10-19 v2 Analysis of PDEs
Abstract
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced by J.M. Lasry and P.L. Lions and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation, from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.
Keywords
Cite
@article{arxiv.1110.3441,
title = {From infinity to one: The reduction of some mean field games to a global control problem},
author = {Olivier Guéant},
journal= {arXiv preprint arXiv:1110.3441},
year = {2011}
}