12 citations · 21 across the 18 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…