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Translation invariant mean field games with common noise. (English) Zbl 1332.60102
Summary: This note highlights a special class of mean field games in which the coefficients satisfy a convolution-type structural condition. A mean field game of this type with common noise is related to a certain mean field game without common noise by a simple transformation, which permits a tractable construction of a solution of the problem with common noise from a solution of the problem without. This yields new existence results for common noise problems, notably allowing controlled volatility, as well as new uniqueness results for problems without common noise.

MSC:
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91A15 Stochastic games, stochastic differential games
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