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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.

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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