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

人工智能（AI）已经应用于许多科学领域，包括成像、计算机视觉和材料科学。然而，将AI应用于不同游戏和经济学的研究仍处于起步阶段。微分对策作为博弈论和最优控制的产物，提供了动态系统中冲突的建模和分析。应用领域包括管理学、经济学、社会科学、生物学和国家安全。其中一个核心目标是计算纳什均衡，即没有玩家有偏离的动机的策略。该研究旨在通过使用、开发和研究适当的机器学习算法来打破计算这些纳什均衡的可追溯性障碍。该项目还为研究生提供研究培训机会。一个主要的瓶颈来自有限玩家博弈的臭名昭著的棘手性，这使得纳什均衡的直接计算非常耗时和内存需求，特别是对于大量玩家。本文通过开发基于博弈的深度神经网络算法，解决了具有有限数量异质参与者的随机微分博弈中高效、准确计算纳什均衡的问题。无限玩家博弈将通过在竞争博弈的平均场博弈理论和合作博弈的平均场控制理论背景下开发的新的强化学习算法来解决。应用到经济和金融问题，如系统性风险和投资/消费被考虑。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.