Differential Games with Asymmetric and Correlated Information

被引:14
作者
Oliu-Barton, Miquel [1 ]
机构
[1] Univ Paris 09, PSL, CEREMADE, F-75016 Paris, France
关键词
Differential games; Fenchel duality; Incomplete information; Comparison principle; Value function; Viscosity solutions; VISCOSITY SOLUTIONS; OPTIMAL STRATEGIES;
D O I
10.1007/s13235-014-0131-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Differential games with asymmetric information were introduced by Cardaliaguet (SIAM J Control Optim 46:816-838, 2007). As in repeated games with lack of information on both sides (Aumann and Maschler in Repeated games with incomplete information, with the collaboration of R. Stearns, 1995), each player receives a private signal (his type) before the game starts and has a prior belief about his opponent's type. Then, a differential game is played in which the dynamic and the payoff functions depend on both types: each player is thus partially informed about the differential game that is played. The existence of the value function and some characterizations have been obtained under the assumption that the signals are drawn independently. In this paper, we drop this assumption and extend these results to the general case of correlated types. As an application, we provide a new characterization of the asymptotic value of repeated games with incomplete information on both sides, as the unique dual solution of a Hamilton-Jacobi equation.
引用
收藏
页码:378 / 396
页数:19
相关论文
共 50 条
[41]   Decomposition of Differential Games with Multiple Targets [J].
Festa, Adriano ;
Vinter, Richard B. .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 169 (03) :848-875
[42]   DIFFERENTIAL GAMES AND ZUBOV'S METHOD [J].
Gruene, Lars ;
Serea, Oana Silvia .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2011, 49 (06) :2349-2377
[43]   Existence of value for differential games with incomplete information and signals on initial states and payoffs [J].
Wu, Xiaochi .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 446 (02) :1196-1218
[44]   An Approach to Stochastic Dynamic Games with Asymmetric Information and Hidden Actions [J].
Ouyang, Yi ;
Tavafoghi, Hamidreza ;
Teneketzis, Demosthenis .
DYNAMIC GAMES AND APPLICATIONS, 2025, 15 (01) :182-215
[45]   Numerical Approximation and Optimal Strategies for Differential Games with Lack of Information on One Side [J].
Cardaliaguet, Pierre .
ADVANCES IN DYNAMIC GAMES AND THEIR APPLICATIONS, 2009, 10 :159-176
[46]   Multiple Pursuers Versus One Evader Reach-Avoid Differential Games With Asymmetric Observations [J].
Fang, Hongwei ;
Yi, Peng ;
Deng, Di ;
He, Bing .
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, 2025, 22 :18605-18616
[47]   Differential games with continuous, switching and impulse controls [J].
Shaiju, A ;
Dharmatti, S .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (01) :23-41
[48]   Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games [J].
Sorin, Sylvain .
DYNAMIC GAMES AND APPLICATIONS, 2011, 1 (01) :172-207
[49]   REFLECTED DIFFERENTIAL GAMES [J].
Serea, Oana-Silvia .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (04) :2516-2532
[50]   Discontinuous games with asymmetric information: An extension of Reny's existence theorem [J].
He, Wei ;
Yannelis, Nicholas C. .
GAMES AND ECONOMIC BEHAVIOR, 2015, 91 :26-35