Monotone numerical methods for finite-state mean-field games

Monotone numerical methods for finite-state mean-field games
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有限状态平均场博弈的单调数值方法

DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
João Saúde
João Saúde
中科院分区：
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文献类型：
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作者：
D. Gomes;João Saúde

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在这里，我们发展了满足单调性条件的有限状态平均场对策(MFGs)的数值方法。MFG由一个具有初值和终值边界条件的微分方程组确定。这些非标准条件是数值逼近解的主要困难。利用单调性条件，我们建立了一个压缩的流，它的不动点解决了定常问题和时间相关问题的MFG。我们用一个MFG模型来说明我们的方法。
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.