Mean field games with congestion

By Yves Achdou, Alessio Porretta. 2017

48 citations recorded by the source corpus.

We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both posed in $(0,T)\times (\mathbb{R}^N /\mathbb{Z}^N)$. Because of congestion and by contrast with simpler cases, the latter system can never be seen as the optimality conditions of an optimal control problem driven by a partial differential equation. The Hamiltonian vanishes as the density tends to $+\infty$ and may not even be defined in the regions where the density is zero. After giving a suitable definition of weak solutions, we prove the existence and uniqueness results of the latter under rather general assumptions. No restriction is made on the horizon $T$.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/361bd106bd06c5ef21bd9a76d6062abba534656f

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In Applied Mathematics

In Finance

Citations in the corpus

Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity (2021, background): “In [36], a notion of monotonicity condition for non-separable Hamiltonians that depend locally on the measure variable was proposed (see also [2]).”