Journal
ANNALS OF PROBABILITY
Volume 44, Issue 6, Pages 3740-3803Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/15-AOP1060
Keywords
Mean field games; stochastic optimal control; McKean Vlasov equations; weak solutions; relaxed controls
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Funding
- NSF [DMS-08-06591, DMS-07-39195]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1211928] Funding Source: National Science Foundation
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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.
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