New Developments in Mean Field Game Theory and Applications

博弈论是研究理性决策者之间战略互动的数学模型。这个项目是关于分析大型人口游戏，这将提高我们对金融，宏观经济和工程中复杂系统的理解，这些系统非常难以分析。在这里，我们将考虑失业保险等应用，并更好地了解金融市场的系统性风险。这些应用程序的结果有可能通过使用这些工具进行风险效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。 该项目将为多名研究生和博士后学者提供支持和机会。近年来，在金融和经济学的启发下，随机控制领域出现了一些令人兴奋的发展：分析大量参与者对整个系统的影响很小的博弈的纳什均衡，导致了平均场博弈理论。现在的应用程序要求更好地理解有限状态平均场游戏，因为这些是计算更顺从，和异构的球员之间的相互作用，使用随机图。该项目具有广泛的应用，如理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。特别是在失业保险的平均场博弈分析、带共同噪声的有限状态平均场博弈、系统性风险长期分析的平均场相互作用、系统性风险长期分析的平均场相互模拟粒子间的异质相互作用/该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查进行评估，被认为值得支持的搜索.

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.