Mean-field games and model predictive control

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

Control of McKean-Vlasov Dynamics versus Mean Field Games

We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which optimization and passage to the limit are performed. When optimizing first, the asymptotic problem is usually referred to as a mean-field game. Otherwise, it ...

Mean field stochastic games for SINR-based medium access control

In this paper we study medium access control with interference management. We formulate a SINR-based dynamic channel access as a stochastic game in which the players adapt their retransmission scheme based on their own backoff state. We analyze the asymptotics of the system using mean field dynamics. Both stable and unstable behaviors are illustrated.