TY - CHAP

T1 - Blackwell-Nash Equilibria in Zero-Sum Stochastic Differential Games

AU - Escobedo-Trujillo, Beatris Adriana

AU - Jasso-Fuentes, Héctor

AU - López-Barrientos, José Daniel

N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Average equilibrium

KW - Bias equilibrium

KW - Blackwell-Nash equilibrium

KW - Laurent series

KW - Zero-sum stochastic differential games

UR - http://www.scopus.com/inward/record.url?scp=85055713582&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-77643-9_5

DO - 10.1007/978-3-319-77643-9_5

M3 - Capítulo

AN - SCOPUS:85055713582

T3 - Progress in Probability

SP - 169

EP - 193

BT - Progress in Probability

PB - Birkhauser

ER -