In this Note, 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.
Dans cette Note nous nous intéressons à un problème particulier de jeu différentiel stochastique de somme non nulle à N joueurs. En utilisant la théorie des équations différentielles stochastiques rétrogrades et le calcul de Malliavin nous donnons la forme explicite d'un équilibre de Nash.
Accepted:
Published online:
Jean-Pierre Lepeltier 1; Zhen Wu 2; Zhiyong Yu 3, 4
@article{CRMATH_2009__347_15-16_959_0,
author = {Jean-Pierre Lepeltier and Zhen Wu and Zhiyong Yu},
title = {Nash equilibrium point for one kind of stochastic nonzero-sum game problem and {BSDEs}},
journal = {Comptes Rendus. Math\'ematique},
pages = {959--964},
publisher = {Elsevier},
volume = {347},
number = {15-16},
year = {2009},
doi = {10.1016/j.crma.2009.04.033},
language = {en},
}
TY - JOUR AU - Jean-Pierre Lepeltier AU - Zhen Wu AU - Zhiyong Yu TI - Nash equilibrium point for one kind of stochastic nonzero-sum game problem and BSDEs JO - Comptes Rendus. Mathématique PY - 2009 SP - 959 EP - 964 VL - 347 IS - 15-16 PB - Elsevier DO - 10.1016/j.crma.2009.04.033 LA - en ID - CRMATH_2009__347_15-16_959_0 ER -
%0 Journal Article %A Jean-Pierre Lepeltier %A Zhen Wu %A Zhiyong Yu %T Nash equilibrium point for one kind of stochastic nonzero-sum game problem and BSDEs %J Comptes Rendus. Mathématique %D 2009 %P 959-964 %V 347 %N 15-16 %I Elsevier %R 10.1016/j.crma.2009.04.033 %G en %F CRMATH_2009__347_15-16_959_0
Jean-Pierre Lepeltier; Zhen Wu; Zhiyong Yu. Nash equilibrium point for one kind of stochastic nonzero-sum game problem and BSDEs. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 959-964. doi : 10.1016/j.crma.2009.04.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.033/
[1] Mathematical Methods of Game and Economic Theory, Studies in Mathematics and Its Applications, North-Holland, Amsterdam, 1976
[2] Stochastic games for N players, J. Optim. Theory Appl., Volume 105 (2000), pp. 543-565
[3] Zero-sum stochastic differential games and backward equations, Systems Control Lett., Volume 24 (1995), pp. 259-263
[4] BSDEs with continuous coefficients and stochastic differential games (El. Karoui; L. Mazliak, eds.), Pitman Research Notes in Mathematics Series, vol. 364, Langman, Harlow, 1997, pp. 115-128
[5] Backward stochastic differential equations in finance, Math. Finance, Volume 7 (1997) no. 1, pp. 1-71
[6] Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Probab., Volume 28 (2000), pp. 558-602
[7] Existence for BSDE with superlinear-quadratic coefficient, Stochastics Stochastics Rep., Volume 63 (1997), pp. 227-240
[8] Equilibrium points in n-person games, Proc. Natl. Acad. Sci. USA, Volume 36 (1950), pp. 48-49
[9] The Malliavin Calculus and Related Topics, Probability and Its Applications, Springer-Verlag, New York and Berlin, 1995
Cited by Sources:
☆ This work is supported by the Natural Science Foundation of China (10671112), the National Basic Research Program of China (973 Program, No. 2007CB814901 and No. 2007CB814904), the Natural Science Foundation of Shandong Province (JQ200801 and 2008BS01024) and the Doctoral Fund of Education Ministry of China.
Comments - Policy