Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

被引：7

作者：

Escobedo-Trujillo, Beatris ^{[1
]}

Lopez-Barrientos, Daniel ^{[1
]}

Hernandez-Lerma, Onesimo ^{[1
]}

机构：

[1] CINVESTAV IPN, Dept Math, Mexico City 07000, DF, Mexico

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2012年 / 153卷 / 03期

关键词：

Average (or ergodic) payoff criteria; Bias optimality; Zero-sum stochastic differential games; Overtaking optimality; DIFFUSIONS; OPTIMALITY; ACCUMULATION;

D O I：

10.1007/s10957-011-9974-4

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper deals with zero-sum stochastic differential games with long-run average payoffs. Our main objective is to give conditions for existence and characterization of bias and overtaking optimal equilibria. To this end, first we characterize the family of optimal average payoff strategies. Then, within this family, we impose suitable conditions to determine the subfamilies of bias and overtaking equilibria. A key step to obtain these facts is to show the existence of solutions to the average payoff optimality equations. This is done by the usual "vanishing discount" approach. Finally, a zero-sum game associated to a certain manufacturing process illustrates our results.

引用

页码：662 / 687

页数：26

共 50 条

[1] Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games
Beatris Escobedo-Trujillo
Daniel López-Barrientos
Onésimo Hernández-Lerma
[J]. Journal of Optimization Theory and Applications, 2012, 153 : 662 - 687
[2] Bias and overtaking equilibria for zero-sum continuous-time Markov games
Tomás Prieto-Rumeau
Onésimo Hernández-Lerma
[J]. Mathematical Methods of Operations Research, 2005, 61 : 437 - 454
[3] Bias and overtaking equilibria for zero-sum continuous-time Markov games
Prieto-Rumeau, T
Hernández-Lerma, O
[J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2005, 61 (03) : 437 - 454
[4] DISCOUNT-SENSITIVE EQUILIBRIA IN ZERO-SUM STOCHASTIC DIFFERENTIAL GAMES
Escobedo-Trujillo, Beatris A.
[J]. JOURNAL OF DYNAMICS AND GAMES, 2016, 3 (01): : 25 - 50
[5] Almost Stationary ∈-Equilibria in Zero-Sum Stochastic Games
J. Flesch
F. Thuijsman
O. J. Vrieze
[J]. Journal of Optimization Theory and Applications, 2000, 105 : 371 - 389
[6] Almost stationary ε-equilibria in zero-sum stochastic games
Flesch, J
Thuijsman, F
Vrieze, OJ
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 105 (02) : 371 - 389
[7] Stochastic zero-sum differential games and backward stochastic differential equations
Oufdil, Khalid
[J]. RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2023, 31 (01) : 65 - 86
[8] On the Minimax Principle and Zero-Sum Stochastic Differential Games
Ho, Y. C.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1974, 13 (03) : 343 - 361
[9] Zero-sum stochastic differential games with reflecting diffusions
Ghosh, MK
Kumar, KS
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 1997, 16 (03): : 237 - 246
[10] Zero-Sum Risk-Sensitive Stochastic Differential Games
Basu, Arnab
Ghosh, Mrinal K.
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 2012, 37 (03) : 437 - 449

← 1 2 3 4 5 →