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

Justina Gianatti; Francisco J. Silva; Ahmad Zorkot

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arXiv · 2305.01445

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

Justina Gianatti·Francisco J. Silva·Ahmad Zorkot

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Abstract

We consider a deterministic mean field games 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.

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Justina Gianatti, Francisco J. Silva, Ahmad Zorkot. 2023-05-02. Approximation of deterministic mean field games under polynomial growth conditions on the data. https://arxiv.org/abs/2305.01445

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