Mean field games with common noise

René Carmona ^[1] ; François Delarue ^[2] ; Daniel Lacker ^[1]
1. [1] Princeton University
  
  Princeton University
  
  Estados Unidos
2. [2] Université de Nice
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 6, 2016, págs. 3740-3803
Idioma: inglés
DOI: 10.1214/15-aop1060
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Resumen
- A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions.