N-Player games and mean-field games with smooth dependence on past absorptions

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

Ergodic Mean Field Games with Hörmander diffusions

I will present joint results with Federica Dragoni (Cardiff University, UK) on existence, uniqueness and regularity of solutions for a class of systems of subelliptic or hypoelliptic PDEs arising from ergodic Mean Field Game models with Hörmander diffusions [5]. These results are applied to the feedback synthesis of Mean Field Game solutions and Nash equilibria of a large class of Nplayer diffe...

Mean-Field Games for Marriage

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple...