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arXiv · 2006.12949

Mean Field Games with monotonous interactions through the law of states and controls of the agents

Z Kobeissi
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Abstract

We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity, with an exponent larger than one. A monotonicity assumption is also made. Existence and uniqueness are proved using a priori estimates which stem from the monotonicity assumptions and Leray-Schauder theorem. Applications of the results are given.

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Z Kobeissi. 2020-06-23. Mean Field Games with monotonous interactions through the law of states and controls of the agents. https://arxiv.org/abs/2006.12949

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