“Cours Bachelier” conferences, though the guiding principle is the same and consists in a progressive introduction of the concepts, methodologies and mathematical tools of mean field game theory. Mean field game theory was created in 2006 by Jean-Michel Lasry and Pierre-Louis Lions and the...
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect t
should be interpreted as that after some time the player is replaced by some new-born one. as the type of reward introduced above is not commonly used in the literature, below we present an example of a situation that can be modeled as a mean-field game with this type of optimality ...
Furthermore, we show that the Bellman equation of ML-POSC can be reduced to the Hamilton–Jacobi–Bellman (HJB) equation by employing a trick from the mean-field control theory [13,14,15]. While the Bellman equation is a functional differential equation, the HJB equation is a partial ...
Furthermore, unlike the mean-field game and control, the coupling of HJB-FP equations is limited to the optimal control function in ML-POSC. By exploiting this property, more efficient algorithms may be proposed for ML-POSC [34]. In this paper, we use the forward–backward sweep method (...
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also inter