Approximation of deterministic mean field games under polynomial growth conditions on the data

GIANATTI, JUSTINA; SILVA, FRANCISCO J.; ZORKOT, AHMAD

Journal of Dynamics and Games

American Institute of Mathematical Sciences

Año: 2024 vol. 11

2164-6066

We consider a deterministic mean field game problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect to the state variable. In this framework, we construct a mean field game problem in discrete time and finite state space that approximates equilibria of the original game. Two numerical examples, solved with the fictitious play method, are presented.