Related papers: The selection problem for some first-order station…
We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master…
This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control and…
In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the equation with a regularized vector field converge to a…
In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak…
We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows…
The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the…
This paper studies a central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude…
This paper is concerned with extending the notion of monotone solution to the mean field game (MFG) master equation to situations in which the coefficients are displacement monotone, instead of the previously introduced notion in the flat…
We study a stationary first--order mean field game on the $d$--dimensional torus. The system couples a Hamilton--Jacobi equation for the value function with a transport equation for the density of players. Our goal is to give a detailed and…
We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work…
In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…
We formulate and investigate a mean field optimization (MFO) problem over a set of probability distributions $\mu$ with a prescribed marginal $m$. The cost function depends on an aggregate term, which is the expectation of $\mu$ with…
This paper presents an axiomatic approach to finite Markov decision processes where the discount rate is zero. One of the principal difficulties in the no discounting case is that, even if attention is restricted to stationary policies, a…
We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount function. In particular, we study (weak)…
The Hamilton-Jacobi-Bellman equation arising from the optimal portfolio selection problem is studied by means of the maximal monotone operator method. The existence and uniqueness of a solution to the Cauchy problem for the nonlinear…
We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also…
Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-order quasi-stationary Mean Field Games system, which involves…
Here, we introduce a price-formation model where a large number of small players can store and trade electricity. Our model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply vs. demand balance…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an $\alpha $-stable process. It is proved that extremal solutions are selected and the respective…