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arXiv · 2002.11055

Nonlocal Bertrand and Cournot Mean Field Games with General Nonlinear Demand Schedule

P. Jameson Graber·Vincenzo Ignazio·Ariel Neufeld
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Abstract

In this article we prove the existence of classical solutions to a system of mean field games arising in the study of exhaustible resource production under market competition. Individual trajectories are modeled by a controlled diffusion process with jumps, which adds a nonlocal term to the PDE system. The assumptions on the Hamiltonian are sufficiently general to cover a large class of examples proposed in the literature on Bertrand and Cournot mean field games. Uniqueness also holds under a sufficient restriction on the structure of the Hamiltonian, which in practice amounts to a small upper bound on the substitutability of goods.

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P. Jameson Graber, Vincenzo Ignazio, Ariel Neufeld. 2020-02-25. Nonlocal Bertrand and Cournot Mean Field Games with General Nonlinear Demand Schedule. https://arxiv.org/abs/2002.11055

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