[Equilibre de Nash pour un jeu de somme non nulle et équations rétrogrades]
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.
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.
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@article{CRMATH_2009__347_15-16_959_0,
author = {Lepeltier, Jean-Pierre and Wu, Zhen and Yu, Zhiyong},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.04.033/}
}
TY - JOUR AU - Lepeltier, Jean-Pierre AU - Wu, Zhen AU - Yu, Zhiyong 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2009.04.033/ DO - 10.1016/j.crma.2009.04.033 LA - en ID - CRMATH_2009__347_15-16_959_0 ER -
%0 Journal Article %A Lepeltier, Jean-Pierre %A Wu, Zhen %A Yu, Zhiyong %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 %U http://www.numdam.org/articles/10.1016/j.crma.2009.04.033/ %R 10.1016/j.crma.2009.04.033 %G en %F CRMATH_2009__347_15-16_959_0
Lepeltier, Jean-Pierre; Wu, Zhen; Yu, Zhiyong. Nash equilibrium point for one kind of stochastic nonzero-sum game problem and BSDEs. Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 959-964. doi : 10.1016/j.crma.2009.04.033. http://www.numdam.org/articles/10.1016/j.crma.2009.04.033/
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☆ 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.
