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XII Symposium of Probability and Stochastic ProcessesBlackwell-Nash Equilibria in Zero-Sum Stochastic Differential Games

XII Symposium of Probability and Stochastic Processes: Blackwell-Nash Equilibria in Zero-Sum... [Advanced-type equilibria for a general class of zero-sum stochastic differential games have been studied in part by Escobedo-Trujillo et al. (J Optim Theory Appl 153:662–687, 2012), in which a comprehensive study of the so-named bias and overtaking equilibria was provided. On the other hand, a complete analysis of advanced optimality criteria in the context of optimal control theory such as bias, overtaking, sensitive discount, and Blackwell optimality was developed independently by Jasso-Fuentes and Hernández-Lerma (Appl Math Optim 57:349–369, 2008; J Appl Probab 46:372–391, 2009; Stoch Anal Appl 27:363–385, 2009). In this work we try to fill out the gap between the aforementioned references. Namely, the aim is to analyze Blackwell-Nash equilibria for a general class of zero-sum stochastic differential games. Our approach is based on the use of dynamic programming, the Laurent series and the study of sensitive discount optimality.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

XII Symposium of Probability and Stochastic ProcessesBlackwell-Nash Equilibria in Zero-Sum Stochastic Differential Games

Part of the Progress in Probability Book Series (volume 73)
Editors: Hernández-Hernández, Daniel; Pardo, Juan Carlos; Rivero, Victor
Escobedo-Trujillo, Beatris Adriana; Jasso-Fuentes, Héctor; López-Barrientos, José Daniel
XII Symposium of Probability and Stochastic Processes — Jun 27, 2018
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References (21)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing AG, part of Springer Nature 2018
ISBN
978-3-319-77642-2
Pages
169 –193
DOI
10.1007/978-3-319-77643-9_5
Publisher site
See Chapter on Publisher Site

Abstract

[Advanced-type equilibria for a general class of zero-sum stochastic differential games have been studied in part by Escobedo-Trujillo et al. (J Optim Theory Appl 153:662–687, 2012), in which a comprehensive study of the so-named bias and overtaking equilibria was provided. On the other hand, a complete analysis of advanced optimality criteria in the context of optimal control theory such as bias, overtaking, sensitive discount, and Blackwell optimality was developed independently by Jasso-Fuentes and Hernández-Lerma (Appl Math Optim 57:349–369, 2008; J Appl Probab 46:372–391, 2009; Stoch Anal Appl 27:363–385, 2009). In this work we try to fill out the gap between the aforementioned references. Namely, the aim is to analyze Blackwell-Nash equilibria for a general class of zero-sum stochastic differential games. Our approach is based on the use of dynamic programming, the Laurent series and the study of sensitive discount optimality.]

Published: Jun 27, 2018

Keywords: Zero-sum stochastic differential games; Average equilibrium; Bias equilibrium; Laurent series; Blackwell-Nash equilibrium; 91A10; 91A15; 91A25

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