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Partial Differential Equation Methods for Mean Field Games

平均场博弈的偏微分方程方法

基本信息

批准号：
1907684
负责人：
David Ambrose
金额：
$ 31.7万
依托单位：
Drexel University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907684&HistoricalAwards=false
关键词：
Partial Differential Equation Methods Mean

项目摘要

Mean field games are models for problems in which a large number of individuals need to make decisions which are related to those of many other individuals. Many applications of mean field games arise from economics. One example to be treated is modeling the decision of households to allocate their income between savings and consumption; the benefits of a household's decision depend on the decisions that the other households make, since the interest rate in this example is determined through the aggregation of the decisions of all the households. This research will seek to understand mathematical theory of these models; this includes proving that the models have solutions and understanding how these solutions depend upon parameters present in the models. Developing the mean field games theory can have impact on the quality of economic forecasts and economic decision-making. Several graduate and undergraduate students will be trained through participation in this research projectExistence and regularity theory will be developed for solutions of mean field games models, and important asymptotic problems will be investigated. The regularity theory includes demonstrating analytic and Gevrey regularity for solutions which have previously been proved to exist with finite Sobolev regularity. Asymptotic regimes include rigorously studying the limit of differential games with finitely many players as the number of players tends to infinity, studying the limit as diffusion parameters vanish, and studying the limit as the time horizon goes to infinity. Problems with nonseparable Hamiltonian and problems arising from applications, such as the household savings problem, will be emphasized. Mean field games systems are taken with initial and terminal data rather than just initial data; tools from initial value problems in areas such as fluid dynamics will be adapted to the forward-backward setting of mean field games.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

平均场博弈（Mean Field Game）是一种模型，用于解决大量个体需要做出与其他许多个体相关的决策的问题。平均场博弈的许多应用来自经济学。要处理的一个例子是对家庭在储蓄和消费之间分配收入的决定进行建模;一个家庭的决定的好处取决于其他家庭的决定，因为在这个例子中，利率是通过所有家庭的决定来确定的。本研究将试图了解这些模型的数学理论;这包括证明模型有解，并了解这些解如何依赖于模型中的参数。平均场博弈理论的发展可以影响经济预测和经济决策的质量。几个研究生和本科生将通过参与本研究项目的培训，存在性和正则性理论将被开发为平均场博弈模型的解决方案，并将研究重要的渐近问题。正则性理论包括证明解析和Gevrey正则性的解决方案，以前已被证明存在有限Sobolev正则性。渐近制度包括严格研究的极限微分游戏与许多球员的球员的数量趋于无穷大，研究的极限扩散参数消失，并研究极限的时间范围趋于无穷大。与不可分的哈密顿量和问题所产生的应用程序，如家庭储蓄问题，将被强调。平均场博弈系统采用初始和终端数据，而不仅仅是初始数据;流体动力学等领域的初始值问题的工具将适用于平均场博弈的前后向设置。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（17）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Existence theory for non-separable mean field games in Sobolev spaces

索博列夫空间中不可分平均场博弈的存在理论

DOI：
10.1512/iumj.2022.71.8900
发表时间：
2022
期刊：
Indiana University Mathematics Journal
影响因子：
1.1
作者：
Ambrose, David
通讯作者：
Ambrose, David

Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

DOI：
10.1088/1361-6544/ad140c
发表时间：
2022-07
期刊：
Nonlinearity
影响因子：
1.7
作者：
D. Ambrose;P. Lushnikov;M. Siegel;Denis A. Silantyev
通讯作者：
D. Ambrose;P. Lushnikov;M. Siegel;Denis A. Silantyev

Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels

粘弹性血管脉动流模型的适定性、不适定性和行波

DOI：
10.1007/s00033-022-01874-x
发表时间：
2022
期刊：
Zeitschrift für angewandte Mathematik und Physik
影响因子：
0
作者：
Kim, Hyeju;Ambrose, David M.
通讯作者：
Ambrose, David M.

Well-posedness and Ill-posedness for Linear Fifth-Order Dispersive Equations in the Presence of Backwards Diffusion

存在向后扩散的线性五阶色散方程的适定性和不适定性

DOI：
10.1007/s10884-020-09905-9
发表时间：
2022
期刊：
Journal of Dynamics and Differential Equations
影响因子：
1.3
作者：
Ambrose, David M.;Woods, Jacob
通讯作者：
Woods, Jacob

Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus

圆环上Navier-Stokes方程的Lei-Lin解的存在性及解析性

DOI：
10.1090/proc/16615
发表时间：
2023
期刊：
Proceedings of the American Mathematical Society
影响因子：
1
作者：
Ambrose, David;Lopes Filho, Milton;Nussenzveig Lopes, Helena
通讯作者：
Nussenzveig Lopes, Helena

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David Ambrose其他文献

The impact of person–environment–occupation transactions on joint attention in children with autism spectrum disorder: A scoping review

人-环境-职业交互对自闭症谱系障碍儿童共同注意力的影响：范围界定审查

DOI：
发表时间：
2020
期刊：
影响因子：
0
作者：
David Ambrose;Diane E MacKenzie;Parisa Ghanouni
通讯作者：
Parisa Ghanouni

Identification, recovery, and impact of ghost fishing gear in the Mullica River-Great Bay Estuary (New Jersey, USA): Stakeholder-driven restoration for smaller-scale systems

DOI：
10.1016/j.marpolbul.2018.10.058
发表时间：
2019-01-01
期刊：
Research article
影响因子：
作者：
Mark Sullivan;Steven Evert;Peter Straub;Melanie Reding;Nathan Robinson;Elizabeth Zimmermann;David Ambrose
通讯作者：
David Ambrose