Existence of value for a differential game with asymmetric information and signal revealing

被引：0
作者：
Xiaochi Wu
机构：
[1] Shandong University,School of Mathematics and Statistics
来源：
International Journal of Game Theory | 2022年 / 51卷
关键词：
Differential Games; Incomplete Information; Signal; Hamilton–Jacobi–Isaacs Equation; 49N30; 49N70; 91A05; 91A10; 91A23;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the present paper, we investigate the existence of value for a new class of infinite horizon two-person zero-sum differential games with asymmetric information on the random pay-off. Before the game begins, both players receive private information about the randomly chosen running cost, while during the game a public signal dependent of the cost function is generated and observed by both players. We prove that, with suitable notion of strategies, the game has a value, and its value function is the unique bounded continuous viscosity solution of a Hamilton–Jacobi–Isaacs equation.
引用
收藏
页码：213 / 247
页数：34
相关论文
共 59 条
[1]  
Bernhard P(1995)Étude d’un jeu de poursuite plane avec connaissance imparfaite d’une coordonnée Automatique-productique informatique industrielle 29 575-601
[2]  
Rapaport A(2011)Some recent aspects of differential game theory Dyn Games Appl 1 74-114
[3]  
Buckdahn R(2013)Value function of differential games without Isaacs’ conditions. an approach with non-anticipative mixed strategies Int J Game Theory 42 989-1020
[4]  
Cardaliaguet P(2015)Differential games with asymmetric information and without Isaacs’ condition Int J Game Theory 46 816-838
[5]  
Quincampoix M(2007)Differential games with asymmetric information SIAM J Control Optim 360 95-107
[6]  
Buckdahn R(2009)A double obstacle problem arising in differential game theory J Math Anal Appl 1 363-375
[7]  
Li J(2014)Pure and random strategies in differential game with incomplete informations J Dyn Games 10 1-16
[8]  
Quincampoix M(2008)Deterministic differential games under probability knowledge of initial condition Int Game Theory Rev 34 769-794
[9]  
Buckdahn R(2009)On a continuous-time game with incomplete information Math Oper Res 59 1-36
[10]  
Quincampoix M(2009)Stochastic differential games with asymmetric information Appl Math Optim 2 206-227
123456