Mean Field Control and Mean Field Game Models with Several Populations

Alain Bensoussan; Tao Huang; Mathieu Laurière

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Mean Field Control and Mean Field Game Models with Several Populations

机译：平均磁场控制和平均场模型与游戏几个数量

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We investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two populations. In the spirit of mean field type control (MFC) problems and mean field games (MFG), each population is approximated by a continuum of infinitesimal agents. We define four different problems in a general context and interpret them in the framework of MFC or MFG. By calculus of variations, we derive formally in each case the adjoint equations for the necessary conditions of optimality. Importantly, we find that in the case of a competition between two coalitions, one needs to rely on a system of master equations in order to describe the equilibrium. Examples are provided, in particular linear-quadratic models for which we obtain systems of ODEs that can be related to Riccati equations.

机译：我们研究两个种群之间的交互与大量的代理。问题在于两个水平:相同的人口,代理之间的相互作用和两个种群之间的相互作用。意思是字段类型的精神控制(MFC)问题和平均场游戏(生产厂)人口是由连续的近似无穷小的代理。一般的上下文和解释他们的问题在MFC框架或制造。变化,我们得到正式在每种情况下伴随方程的必要条件最优。两个联盟之间的竞争需要依赖于系统的主方程为了描述平衡。提供,特别是线性二次模型我们获得系统的常微分方程相关的黎卡提微分方程。

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来源
《Minimax theory and its applications》 |2018年第2期|173-209|共37页
作者
Alain Bensoussan; Tao Huang; Mathieu Laurière;
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作者单位

Department of Operations Research and Financial Engineering, Princeton University, Charlton Street, Princeton, NJ 08544, U.S.A.;

Dept. of Mathematics, Wayne State University, 4841 Cass Avenue, Detroit, MI 48201, U.S.A.;

International Center for Decision and Risk Analysis, Jindal School of Management, University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080, U.S.A.;

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原文格式 PDF
正文语种英语
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关键词
field control; Riccati equations; Master equationAgentsMean-field theoryHamilton-Jacobi equationmean field strength;

机译：现场控制,黎卡提微分方程;主人equationAgentsMean-field theoryHamilton-Jacobiequationmean场强;

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Mean Field Control and Mean Field Game Models with Several Populations

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