  In this paper, we study Nash equilibrium payoffs for nonzero-sum stochastic
differential games via the theory of backward stochastic differential
equations. We obtain an existence theorem and a characterization theorem of
Nash equilibrium payoffs for nonzero-sum stochastic differential games with
nonlinear cost functionals defined with the help of a doubly controlled
backward stochastic differential equation. Our results extend former ones by
Buckdahn, Cardaliaguet and Rainer (2004) and are based on a backward stochastic
differential equation approach.
