Monotone numerical methods for finite-state mean-field games

Publication Year:
2017
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Repository URL:
http://hdl.handle.net/10754/626519
Author(s):
Gomes, Diogo A.; Saude, Joao
Publisher(s):
arXiv
preprint description
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.