Risk-sensitive Markov stopping games with an absorbing state

Jaicer López-Rivero; Rolando Cavazos-Cadena; Hugo Cruz-Suárez

Kybernetika (2022)

  • Volume: 58, Issue: 1, page 101-122
  • ISSN: 0023-5954

Abstract

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This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I. The performance of a pair of decision strategies is measured by the risk-sensitive (expected) total reward of player I and, besides mild continuity-compactness conditions, the main structural assumption on the model is the existence of an absorbing state which is accessible from any starting point. In this context, it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established.

How to cite

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López-Rivero, Jaicer, Cavazos-Cadena, Rolando, and Cruz-Suárez, Hugo. "Risk-sensitive Markov stopping games with an absorbing state." Kybernetika 58.1 (2022): 101-122. <http://eudml.org/doc/297915>.

@article{López2022,
abstract = {This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I. The performance of a pair of decision strategies is measured by the risk-sensitive (expected) total reward of player I and, besides mild continuity-compactness conditions, the main structural assumption on the model is the existence of an absorbing state which is accessible from any starting point. In this context, it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established.},
author = {López-Rivero, Jaicer, Cavazos-Cadena, Rolando, Cruz-Suárez, Hugo},
journal = {Kybernetika},
keywords = {monotone operator; fixed point; equilibrium equation; hitting time; bounded rewards; certainty equivalent},
language = {eng},
number = {1},
pages = {101-122},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Risk-sensitive Markov stopping games with an absorbing state},
url = {http://eudml.org/doc/297915},
volume = {58},
year = {2022},
}

TY - JOUR
AU - López-Rivero, Jaicer
AU - Cavazos-Cadena, Rolando
AU - Cruz-Suárez, Hugo
TI - Risk-sensitive Markov stopping games with an absorbing state
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 1
SP - 101
EP - 122
AB - This work is concerned with discrete-time Markov stopping games with two players. At each decision time player II can stop the game paying a terminal reward to player I, or can let the system to continue its evolution. In this latter case player I applies an action affecting the transitions and entitling him to receive a running reward from player II. It is supposed that player I has a no-null and constant risk-sensitivity coefficient, and that player II tries to minimize the utility of player I. The performance of a pair of decision strategies is measured by the risk-sensitive (expected) total reward of player I and, besides mild continuity-compactness conditions, the main structural assumption on the model is the existence of an absorbing state which is accessible from any starting point. In this context, it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established.
LA - eng
KW - monotone operator; fixed point; equilibrium equation; hitting time; bounded rewards; certainty equivalent
UR - http://eudml.org/doc/297915
ER -

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