Nash Equilibria in a class of Markov stopping games

Cavazos-Cadena, Rolando, and Hernández-Hernández, Daniel. "Nash Equilibria in a class of Markov stopping games." Kybernetika 48.5 (2012): 1027-1044. <http://eudml.org/doc/251394>.

@article{Cavazos2012,
abstract = {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.},
author = {Cavazos-Cadena, Rolando, Hernández-Hernández, Daniel},
journal = {Kybernetika},
keywords = {zero-sum stopping game; equality of the upper and lower value functions; contractive operator; hitting time; stationary strategy; zero-sum stopping game; equality of the upper and lower value functions; contractive operator; hitting time; stationary strategy},
language = {eng},
number = {5},
pages = {1027-1044},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Nash Equilibria in a class of Markov stopping games},
url = {http://eudml.org/doc/251394},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Cavazos-Cadena, Rolando
AU - Hernández-Hernández, Daniel
TI - Nash Equilibria in a class of Markov stopping games
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 5
SP - 1027
EP - 1044
AB - 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.
LA - eng
KW - zero-sum stopping game; equality of the upper and lower value functions; contractive operator; hitting time; stationary strategy; zero-sum stopping game; equality of the upper and lower value functions; contractive operator; hitting time; stationary strategy
UR - http://eudml.org/doc/251394
ER -