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# Mean-field type FBSDEs in a domination-monotonicity framework and LQ multi-level Stackelberg games

This work is supported in part by the National Key R&D Program of China (Grant No. 2018YFA0703900) and the National Natural Science Foundation of China (Grant No. 11871310).

• Motivated by various mean-field type linear-quadratic (MF-LQ, for short) multi-level Stackelberg games, we propose a kind of multi-level self-similar randomized domination-monotonicity structures. When the coefficients of a class of mean-field type forward-backward stochastic differential equations (MF-FBSDEs, for short) satisfy this kind of structures, we prove the existence, the uniqueness, an estimate and the continuous dependence on the coefficients of solutions. Further, the theoretical results are applied to construct unique Stackelberg equilibria for forward and backward MF-LQ multi-level Stackelberg games, respectively.

Mathematics Subject Classification: 60H10, 49N10, 93E20.

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