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<p style='text-indent:20px;'>We study mean-field doubly reflected BSDEs. First, using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-integrable with <inline-formula><tex-math id="M2">\begin{document}$ p = 1 $\end{document}</tex-math></inline-formula> or <inline-formula><tex-math id="M3">\begin{document}$ p&gt;1 $\end{document}</tex-math></inline-formula>. The two cases are treated separately. Next by penalization we show also the existence of the solution. The two methods do not cover the same set of assumptions.</p>

We study mean-field doubly reflected BSDEs. Using the fixed point method, we show existence and uniqueness of the solution when the data which define the BSDE are p-integrable with p = 1 or p > 1. The two cases are treated separately. CONTENTS 1. Introduction 1 2. Notations and formulation of the problems 2 2.1. Notations 2 2.2. The class of doubly reflected BSDEs 3 2.3. Assumptions on ( f , ξ, h, g) 3 3. Existence and Uniqueness of a Solution of the Doubly Reflected BSDE of Mean-Field type 4 3.1. The case p > 1 4 3.2. The case p=1 9 References 12

We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.

We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.