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A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals. (English) Zbl 1237.60047
This paper considers a backward stochastic differential equation (BSDE) approach to discuss two-player, non-zero-sum, stochastic differential games. The main advantage of the BSDE approach is its flexibility in accommodating non-Markovian control processes and controlled state processes. In the paper, the authors establish an existence theorem and a characterization theorem for the Nash equilibrium payoffs of the games by invoking the use of doubly controlled BSDEs.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 91A23 Differential games (aspects of game theory) 91A15 Stochastic games, stochastic differential games
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