COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Variational Mean Field Games

## Variational Mean Field GamesAdd to your list(s) Download to your calendar using vCal - Filippo Santambrogio (Université Paris Sud)
- Monday 03 April 2017, 15:00-16:00
- CMS, MR13.
If you have a question about this talk, please contact Mikaela Iacobelli. I will give a brief introduction to the the emerging topic of Mean Field Games, introduced some years ago (by two groups at the same time: Huang, Malhamé and Caines, but also Lasry and Lions, who then devoted 6 subsequent editions of his course at Collège de France to its mathematical analysis) as a model for the equilibrium of a population of agents each selecting his own optimal paths, according to a criterion which involves the density of the other agents, in the form of a congestion cost. This gives rise to a coupled system of PDEs, a continuity equation where the density moves according to the gradient of a value function, and a Hamilton-Jacobi equation solved by the value function, where the density also appears. I will mainly deal with the case where this equilibrium problem may be seen as optimality conditions of a convex variational problem, and give the main results in this framework. In particular, I will present some easy but recent regularity results, as well as the connection with optimal transport theory. These results are also needed to make rigorous the connection between optimality and equilibrium and allow for an interesting extension where instead of penalizing higher densities we insert a density constraint. Globally, the talk will be based on papers in collaborations with P. Cardaliaguet, A. Mészáros, J.-D. Benamou, G. Carlier, A. Prosinski and H. Lavenant. This talk is part of the Geometric Analysis and Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- CMS, MR13
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Geometric Analysis and Partial Differential Equations seminar
- School of Physical Sciences
Note that ex-directory lists are not shown. |
## Other listsElectrical Engineering Division Talks Mathematics and Machine Learning Cambridge Neurological Society## Other talksChildhood adversity and chronic disease: risks, mechanisms and resilience Prof Kate Jones (UCL): Biodiversity & Conservation My Life in Science Seminar 'Gene regulation in the innate and adaptive immune systems' Finding meaning in English writing Identifying new gene regulating networks in immune cells |