Geodesic
Nash Equilibria in a class of Markov stopping games
Kybernetika, Tome 48 (2012) no. 5, pp. 1027-1044

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

This work concerns a class of discrete-time, zero-sum games with two players and Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I and, if the system is no halted, player I selects an action to drive the system and receives a running reward from player II. Measuring the performance of a pair of decision strategies by the total expected discounted reward, under standard continuity-compactness conditions it is shown that this stopping game has a value function which is characterized by an equilibrium equation, and such a result is used to establish the existence of a Nash equilibrium. Also, the method of successive approximations is used to construct approximate Nash equilibria for the game.
Classification : 91A10, 91A15
Keywords: zero-sum stopping game; equality of the upper and lower value functions; contractive operator; hitting time; stationary strategy 
@article{KYB_2012__48_5_a13,
     author = {Cavazos-Cadena, Rolando and Hern\'andez-Hern\'andez, Daniel},
     title = {Nash {Equilibria} in a class of {Markov} stopping games},
     journal = {Kybernetika},
     pages = {1027--1044},
     publisher = {mathdoc},
     volume = {48},
     number = {5},
     year = {2012},
     mrnumber = {3086867},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a13/}
}
TY  - JOUR
AU  - Cavazos-Cadena, Rolando
AU  - Hernández-Hernández, Daniel
TI  - Nash Equilibria in a class of Markov stopping games
JO  - Kybernetika
PY  - 2012
SP  - 1027
EP  - 1044
VL  - 48
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a13/
LA  - en
ID  - KYB_2012__48_5_a13
ER  - 
%0 Journal Article
%A Cavazos-Cadena, Rolando
%A Hernández-Hernández, Daniel
%T Nash Equilibria in a class of Markov stopping games
%J Kybernetika
%D 2012
%P 1027-1044
%V 48
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a13/
%G en
%F KYB_2012__48_5_a13
Cavazos-Cadena, Rolando; Hernández-Hernández, Daniel. Nash Equilibria in a class of Markov stopping games. Kybernetika, Tome 48 (2012) no. 5, pp. 1027-1044. http://geodesic.mathdoc.fr/item/KYB_2012__48_5_a13/