Monotone solutions for mean field games master equations: finite state space and optimal stopping
Monotone solutions for mean field games master equations: finite state space and optimal stopping
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DOI：
10.5802/jep.167
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发表时间：
2020-07
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影响因子：
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通讯作者：
Charles Bertucci
中科院分区：
文献类型：
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作者：
Charles Bertucci
提出了平均场对策主方程解的新概念。这个概念允许我们处理仅仅是连续的解。我们证明了这种解决方案的唯一性和稳定性的第一个结果。结果表明，这一概念有助于刻画最优停止或脉冲控制的平均场博弈的价值函数，这是本文后半部分的主题。我们引入的解的概念只在单调的情况下有用。本文主要研究有限状态空间的情形。
We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that this notion is helpful to characterize the value function of mean field games of optimal stopping or impulse control and this is the topic of the second half of this paper. The notion of solution we introduce is only useful in the monotone case. We focus in this paper in the finite state space case.