Mathematics

Some estimates for stationary extended mean field games

V. K. Voskanyan^a, D. Gomes<sup>b

a</sup> Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan
^b Instituto Superior Técnico, Universidade Técnica de Lisboa

Abstract: Mean field games theory is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play noncooperative dynamic games under certain symmetry assumptions. In this paper we consider quasivariational mean field games system with additional dependence on a velocity field of the players. We obtain certain estimates for the solutions to this system. In a forthcoming paper we intend to obtain an existence result using this kind of estimates and continuation method.

Keywords: mean field games, quasivariational, velocity field dependence, stationary.

MSC: 49N70; 35B45, 35J47, 91A13

Received: 29.09.2012
Accepted: 12.11.2012

Language: English