Special Session 184: Mean-Field Games: From Partial Differential Equations to Numerical Methods

Ergodic Mean Field Games of Controls with State Constraints
Kyle Rosengartner
Baylor University
USA
Co-Author(s):    Jameson Graber
Abstract:
In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players` states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints, in which equilibria are characterized by solutions to a second-order MFGC system where the value function blows up at the boundary, the density of players vanishes at a commensurate rate, and the joint distribution of states and controls satisfies the appropriate fixed-point relation. We prove that such systems are well-posed in the case of monotone coupling and Hamiltonians with at most quadratic growth.