Mathematical Description for Information Pattern of Discrete-Time Two-Person Stochastic Differential Games

FONT face; Verdana; FAN Hong-qi; WANG Sheng; FU Qiang; FONT

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Mathematical Description for Information Pattern of Discrete-Time Two-Person Stochastic Differential Games

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- Mathematical Description for Information Pattern of Discrete-Time Two-Person Stochastic Differential Games
- Acta Electronica Sinica Vol. 38, Issue 6, Pages: 1355-1361(2010)
- 作者机构：
  
  （国防科技大学ATR实验室, ）,湖南,长沙,410073
- 作者简介：
- 基金信息：
- DOI：
  CLC： O231;TP273+.1
- Published：2010
- 稿件说明：
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FONT face, Verdana, FAN Hong-qi, et al. Mathematical Description for Information Pattern of Discrete-Time Two-Person Stochastic Differential Games[J]. Acta Electronica Sinica, 2010, 38(6): 1355-1361.
DOI：

FONT face, Verdana, FAN Hong-qi, et al. Mathematical Description for Information Pattern of Discrete-Time Two-Person Stochastic Differential Games[J]. Acta Electronica Sinica, 2010, 38(6): 1355-1361. DOI：

摘要

<FONT face=Verdana>在离散时间二人随机微分对策问题研究中，信息模式概念尚缺乏统一而准确的描述. 针对这一问题，首先将Witsenhausen关于信息模式的相关概念应用到该问题，从数学上严格定义了信息模式及其相关概念；然后对几种典型信息模式的性质及相应对策问题最优解的结构形式作出了严格的证明. 相关概念与性质为离散时间二人随机微分对策问题的研究提供了重要的理论工具.

Abstract

<FONT face=Verdana>In the researches of discrete-time two-person stochastic differential games

the uniform and exact descriptions on information pattern are absent. To solve this problem，the mathematical definitions of information pattern and other related concepts are addressed in this paper firstly

by introducing Witsenhausen’s concepts about information pattern to the discrete-time two-person stochastic differential games. Then the properties of several typical information patterns and the structures of optimal control law of differential game under these information patterns are strictly proved. The concepts and theorems of the paper provide an important theoretical tool for the researches of discrete-time two-person stochastic differential games.

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