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arXiv · 1705.00174

Monotone numerical methods for finite-state mean-field games

Diogo Gomes·Joao Saude
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Abstract

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.

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Diogo Gomes, Joao Saude. 2017-04-29. Monotone numerical methods for finite-state mean-field games. https://arxiv.org/abs/1705.00174

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