Denumerable Markov stopping games with risk-sensitive total reward criterion

Manuel A. Torres-Gomar; Rolando Cavazos-Cadena; Hugo Cruz-Suárez

Kybernetika (2024)

  • Volume: 60, Issue: 1, page 1-18
  • ISSN: 0023-5954

Abstract

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This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established.

How to cite

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Torres-Gomar, Manuel A., Cavazos-Cadena, Rolando, and Cruz-Suárez, Hugo. "Denumerable Markov stopping games with risk-sensitive total reward criterion." Kybernetika 60.1 (2024): 1-18. <http://eudml.org/doc/299378>.

@article{Torres2024,
abstract = {This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established.},
author = {Torres-Gomar, Manuel A., Cavazos-Cadena, Rolando, Cruz-Suárez, Hugo},
journal = {Kybernetika},
keywords = {monotone operator; fixed point; equilibrium equation; Nash equilibrium; hitting time; bounded rewards},
language = {eng},
number = {1},
pages = {1-18},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Denumerable Markov stopping games with risk-sensitive total reward criterion},
url = {http://eudml.org/doc/299378},
volume = {60},
year = {2024},
}

TY - JOUR
AU - Torres-Gomar, Manuel A.
AU - Cavazos-Cadena, Rolando
AU - Cruz-Suárez, Hugo
TI - Denumerable Markov stopping games with risk-sensitive total reward criterion
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
VL - 60
IS - 1
SP - 1
EP - 18
AB - This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established.
LA - eng
KW - monotone operator; fixed point; equilibrium equation; Nash equilibrium; hitting time; bounded rewards
UR - http://eudml.org/doc/299378
ER -

References

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