12 citations · 21 across the 18 of their papers we have counts for
22 papers
Mean field games as a tool for AI safety: a worked example from the July 2026 Hugging Face incident
P. Jameson Graber
One way to make AI systems safe is to shape what the system is: its objective and dispositions. We take a complementary route: treat the agents' characteristics as partly unknown a…
Mean Field Games of Controls with Boundary Conditions & Invariance Constraints
P. Jameson Graber, Kyle Rosengartner
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their cont…
Control on Hilbert Space and Mean Field Control: the Common Noise Case
Alain Bensoussan, P. Jameson Graber, Phillip Yam
The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \cite{CDLL}, following the approach of contro…
A Model Problem for First Order Mean Field Games with Discrete Initial Data
P. Jameson Graber, Brady Zimmerman
In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their…
On monotonicity conditions for Mean Field Games
P. Jameson Graber, Alpár R. Mészáros
In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $…
On Some Mean Field Games and Master Equations through the lens of conservation laws
P. Jameson Graber, Alpár R. Mészáros
In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and mast…
Master Equation for Cournot Mean Field Games of Control with Absorption
P. Jameson Graber, Ronnie Sircar
We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of…
Parameter sensitivity analysis for mean field games of production
P. Jameson Graber, Marcus Laurel
We study a mean field game system introduced by Chan and Sircar (AMO, 2015) to model production of an exhaustible resource. In particular, we study the sensitivity of the solution…
Weak Solutions for Potential Mean Field Games of Controls
Jameson Graber, Alan Mullenix, Laurent Pfeiffer
We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many neg…
Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics
Fabio S. Bemfica, Marcelo M. Disconzi, P. Jameson Graber
We study the theory of relativistic viscous hydrodynamics introduced in arXiv:1109.0985 and arXiv:1907.12695, which provided a causal and stable first-order theory of relativistic…
Control on Hilbert Spaces and Application to Some Mean Field Type Control Problems
Alain Bensoussan, P. Jameson Graber, Sheung Chi Phillip Yam
We propose a new approach to studying classical solutions of the Bellman equation and Master equation for mean field type control problems, using a novel form of the "lifting" idea…
Stochastic Control on Space of Random Variables
Alain Bensoussan, P. Jameson Graber, S. C. P. Yam
By extending \cite{bensoussan2015control}, we implement the proposal of Lions \cite{lions14} on studying mean field games and their master equations via certain control problems on…
The planning problem in Mean Field Games as regularized mass transport
P. Jameson Graber, Alpár R. Mészáros, Francisco J. Silva +1
In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak…
Sobolev regularity for first order Mean Field Games
P. Jameson Graber, Alpár R. Mészáros
In this paper we obtain Sobolev estimates for weak solutions of first oder variational Mean Field Game systems with coupling terms that are local function of the density variable.…
Variational mean field games for market competition
P. Jameson Graber, Charafeddine Mouzouni
In this paper, we explore Bertrand and Cournot Mean Field Games models for market competition with reflection boundary conditions. We prove existence, uniqueness and regularity of…
Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource
P. Jameson Graber
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward…
Existence and uniqueness of solutions for Bertrand and Cournot mean field games
P. Jameson Graber, Alain Bensoussan
We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a p…
Weak solutions for mean field games with congestion
Philip Jameson Graber
We study the short-time existence and uniqueness of solutions to a coupled system of partial differential equations arising in mean field game theory. It has the generic form $$ \l…
Rotation Remainders
Philip Jameson Graber
We study properties of an array of numbers, called "the triangle," in which each row is formed by rotating all the numbers in the previous row to the left by positions in cycli…
Second order mean field games with degenerate diffusion and local coupling
Pierre Cardaliaguet, J. Graber, Alessio Porretta +1
We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is no…
Mean field games systems of first order
Pierre Cardaliaguet, Philip Jameson Graber
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and…
Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonian
Philip Jameson Graber
We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the p…