Collaborative Research: Machine Learning Theory and Algorithms for Differential Games, with Applications in Economics

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Artificial intelligence (AI) has been applied in many scientific fields, including imaging, computer vision, and materials science. However, the study of the application of AI to differential games and economics is still in its infancy. Differential games, as an offspring of game theory and optimal control, provide the modeling and analysis of conflicts in the context of a dynamical systems. Domains of applications include management science, economics, social science, biology, and national security. One of the core objectives is to compute Nash equilibria that refer to strategies by which no player has an incentive to deviate. The research aims to break the tractability barrier in computing these Nash equilibria by using, developing, and studying appropriate Machine Learning algorithms. The project also provides research training opportunities for graduate students. A major bottleneck comes from the notorious intractability of finite-player games, which makes the direct computation of Nash equilibria extremely time-consuming and memory demanding, especially for a large number of players. The problem of efficiently and accurately computing Nash equilibria for stochastic differential games with a finite number of heterogeneous players is addressed by developing play-based Deep Neural Networks algorithms. Infinite-player games will be solved by new Reinforcement Learning algorithms developed in the context of Mean Field Game theory for competitive games and Mean Field Control theory for cooperative games. Applications to economics and finance problems such as Systemic Risk and Investment/Consumption are considered.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.