New Developments in Mean Field Game Theory and Applications

平均场博弈论及其应用的新进展

基本信息

批准号：
2106556
负责人：
Erhan Bayraktar
金额：
$ 33万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2106556&HistoricalAwards=false
关键词：
New Developments Mean Field Game

项目摘要

Game theory is the study of mathematical models of strategic interaction among rational decision-makers. This project is about analyzing large population games, which will improve our understanding of complex systems in finance, macro-economics and engineering that are known to be extremely difficult to analyze. Here we will consider applications such as unemployment insurance and better understanding of systemic risk in financial markets. Results on these applications have a potential to help regulators with their decision making by using these tools to conduct risk-benefit analyses. The tools developed here will also be applicable to answering broader fundamental questions in mathematical finance. This project will provide support and opportunities for several graduate students and postdoctoral scholars.There have been some exciting developments in stochastic control inspired by finance and economics in the recent years: The analysis of Nash equilibriums of games with large number of players each having a very little influence on the overall system lead to the theory of mean field games. Applications now mandate finer understanding of finite state mean field games, since these are computationally more amenable, and heterogenous interactions between players using random graphs. The project has broad applications such as understanding macro-economic problems and systemic risk. The proposal will contribute to these developments by providing some new mathematical tools and exciting new results. In particular we propose to make advances in the following problems: Mean-field game analysis of Unemployment Insurance; Finite State Mean Field Games with Common Noise; Mean Field Interaction to analyze Systemic Risk in the long run; Modeling Heterogenous Interactions among particles/agents.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.

博弈论是对理性决策者之间战略互动的数学模型的研究。该项目旨在分析大型人口博弈，这将提高我们对金融、宏观经济和工程领域复杂系统的理解，而众所周知，这些系统极难分析。在这里，我们将考虑失业保险等应用以及更好地理解金融市场的系统性风险。这些应用的结果有可能通过使用这些工具进行风险收益分析来帮助监管机构做出决策。这里开发的工具也将适用于回答数学金融中更广泛的基本问题。该项目将为几位研究生和博士后学者提供支持和机会。近年来，受金融和经济学的启发，随机控制领域取得了一些令人兴奋的进展：对整个系统的影响很小，从而产生了平均场博弈理论。现在的应用程序要求更好地理解有限状态平均场游戏，因为这些游戏在计算上更容易接受，并且使用随机图的玩家之间的异构交互。该项目具有广泛的应用，例如了解宏观经济问题和系统性风险。该提案将通过提供一些新的数学工具和令人兴奋的新结果来促进这些发展。我们特别建议在以下问题上取得进展：失业保险的平均场博弈分析；具有共同噪声的有限状态平均场博弈；平均场相互作用分析长期系统风险；模拟粒子/介质之间的异质相互作用。该奖项反映了 NSF 的法定使命，并且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。