By introducing a stochastic differential game whose dynamics and multi-dimensional cost functionals form a multi-dimensional fully coupled forward-backward stochastic differential equation with jumps, we give a probabilistic interpretation to a system of coupled Hamilton-Jacobi-Bellman-Isaacs equations. For this, we generalize the definition of the value function initially defined only for deterministic times and states to stopping times and random variables. The generalization plays a key role in the proof of a strong dynamic programming principle. This strong dynamic programming principle allows us to show that the value function is a viscosity solution of our system of coupled HJBI equations. The uniqueness is obtained for a particular but important case.

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