Graphon Mean Field Games and Their Equations

Graphon games

The study of strategic behavior in large scale networks via standard game theoretical methods is a challenging, if not intractable, task. In this paper, we propose a way to approximate games played over networks of increasing size, by using the graph limiting concept of graphon. To this end, we introduce the new class of graphon games for populations of infinite size. We investigate existence a...

Mean field games equations with quadratic Hamiltonian: a specific approach

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to +∞, have been introduced by J.-M. Lasry and P.-L. Lions in [11, 12, 13]. We use a change of variables to transform the mean field games (MFG) equations into a system of simpler coupled partial differential equations, in the case of a quadratic Hamiltonian. This system...

Mean Field Games

We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects. . . ). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited inform...

Discrete mean field games

In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality criteria. The mean field approach for optimal control and differential games (continuous state and time) was introduced by Lasry and Lions [LL06a, LL06b, LL07]. ...

Mean field games and applications