Mean field games of controls: Propagation of monotonicities

IF 1 2区 数学 Q3 STATISTICS & PROBABILITY
Chenchen Mou, Jianfeng Zhang
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引用次数: 3

Abstract

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity conditions are crucial to guarantee the uniqueness of mean field equilibria and then the global wellposedness for master equations. In the literature the monotonicity condition could be the Lasry–Lions monotonicity, the displacement monotonicity, or the anti-monotonicity conditions. In this paper, we investigate these three types of monotonicity conditions for Mean Field Games of Controls and show their propagation along the solutions to the master equations with common noises. In particular, we extend the displacement monotonicity to semi-monotonicity, whose propagation result is new even for standard mean field games. This is the first step towards the global wellposedness theory for master equations of Mean Field Games of Controls.
控制的平均场对策:单调性的传播
控制的平均场博弈理论考虑了一类通过状态和控制的联合分布进行交互的平均场博弈。众所周知,对于标准平均场对策,一定的单调性条件对于保证平均场平衡点的唯一性,进而保证主方程的全局适定性是至关重要的。在文献中,单调性条件可以是Lasry-Lions单调性、位移单调性或反单调性条件。本文研究了控制的平均域对策的这三种单调性条件,并给出了它们沿带共同噪声的主方程解的传播。特别地,我们将位移单调性推广到半单调性,其传播结果是新的,即使对于标准平均场对策也是如此。这是向控制平均场博弈主方程的全局适定性理论迈出的第一步。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.60
自引率
13.30%
发文量
29
审稿时长
12 weeks
期刊介绍: Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1). Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.
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