  In this paper we investigate Nash equilibrium payoffs for two-player
nonzero-sum stochastic differential games whose cost functionals are defined by
a system of coupled backward stochastic differential equations. We obtain an
existence theorem and a characterization theorem for Nash equilibrium payoffs.
For this end the problem is described equivalently by a stochastic differential
game with jumps. But, however, unlike the work by Buckdahn, Hu and Li [9], here
the important tool of a dynamic programming principle for stopping times has to
be developed. Moreover, we prove that the lower and upper value functions are
the viscosity solutions of the associated coupled systems of PDEs of Isaacs
type, respectively. Our results generalize those by Buckdahn, Cardaliaguet and
Rainer [7] and by Lin [16].
