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 -