Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to study Nash equilibria for such problems in the limit when the number of players is infinite. The theory has been extensively developed in the past decade, using both analytical and probabilistic tools, and a wide range of applications have been discovered, from economics to crowd motion. More recently the interaction with machine learning has attracted a growing interest. This aspect is particularly relevant to solve very large games with complex structures, in high dimension or with common sources of randomness. In this chapter, we review the literature on the interplay between mean field games and deep learning, with a focus on three families of methods. A special emphasis is given to financial applications.
翻译:金融市场和更广泛的宏观经济模式涉及大量个人,他们通过各种变数进行互动,如所有代理人的合计行为所产生的价格等。在玩家人数无限的限度内,引入了模拟野外游戏来研究纳什的平衡性。在过去十年里,该理论得到了广泛发展,使用了分析工具和概率工具,并发现了从经济学到人群运动的广泛应用。最近,与机器学习的互动引起了越来越多的兴趣。这个方面对于用复杂结构、高维度或共同随机性来源解决非常大型的游戏尤为重要。在本章中,我们审查了关于中等野外游戏和深层次学习之间相互作用的文献,重点是三种方法的组合。特别强调了金融应用。