New Developments in Mean Field Game Theory and Applications

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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.