Theory, Implementations, and Applications of Mean Field Games: the Second Generation
Abstract
Since its inception about a decade ago, the theory of Mean Field Games has rapidly developed into one of the most significant and exciting source of progress in the equilibrium analysis of complex systems. The introduction of ideas from statistical physics in the search for approximate equilibria created a new wave of interest in the study of large populations of competitive individuals with mean field interactions. The search for equilibria in a mean field game is an attempt to identify and quantify global characteristics (macroscopic behavior) of large populations of individuals optimizing their own cost-reward trade os (microscopic behavior). The challenge is to understand and quantify the way in which the behavior of rational individuals who may not see the big picture does affect the overall conduct of the population. Propagation of chaos (which implies asymptotic independence) and rational irrationality (to emphasize the fact that rational decisions at the individual level can lead to irrationality at the global level) have often been used to describe some of the possible outcomes. This broad brush description has its parallel in the structure of the analytical and numerical tools used to study these phenomena. The proposal aims at the development of new stochastic and numerical methods for these equilibrium analyses. Motivated by a wide spectrum of applications ranging from population dynamics and social networks, to communications and cyber security, it will advance the understanding of complex stochastic systems by introducing and developing new mathematical theories and associated computational algorithms.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 14, 2022
- Source ID
- FA95501910291
Entities
People
- René Carmona
Organizations
- Air Force Office of Scientific Research
- Trustees of Princeton University
- United States Air Force