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Nash equilibrium point for one kind of stochastic nonzero-sum game problem and BSDEs. (English. Abridged French version) Zbl 1173.91310
Summary: We deal with one kind of stochastic nonzero-sum differential game problem for \(N\) players. Using the theory of backward stochastic differential equations and Malliavin calculus, we give the explicit form of a Nash equilibrium point.

MSC:
91A15 Stochastic games, stochastic differential games
91A23 Differential games (aspects of game theory)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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[1] Aubin, J.P., Mathematical methods of game and economic theory, Studies in mathematics and its applications, (1976), North-Holland Amsterdam
[2] Bensoussan, A.; Frehse, J., Stochastic games for N players, J. optim. theory appl., 105, 543-565, (2000) · Zbl 0977.91006
[3] Hamadène, S.; Lepeltier, J.P., Zero-sum stochastic differential games and backward equations, Systems control lett., 24, 259-263, (1995) · Zbl 0877.93125
[4] Hamadène, S.; Lepeltier, J.P.; Peng, S., BSDEs with continuous coefficients and stochastic differential games, (), 115-128 · Zbl 0892.60062
[5] El Karoui, N.; Peng, S.; Quenez, M.C., Backward stochastic differential equations in finance, Math. finance, 7, 1, 1-71, (1997) · Zbl 0884.90035
[6] Kobylanski, M., Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. probab., 28, 558-602, (2000) · Zbl 1044.60045
[7] Lepeltier, J.P.; San Martin, J., Existence for BSDE with superlinear-quadratic coefficient, Stochastics stochastics rep., 63, 227-240, (1997) · Zbl 0910.60046
[8] Nash, J., Equilibrium points in n-person games, Proc. natl. acad. sci. USA, 36, 48-49, (1950) · Zbl 0036.01104
[9] Nualart, D., The Malliavin calculus and related topics, Probability and its applications, (1995), Springer-Verlag New York and Berlin · Zbl 0837.60050
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