@article{López-Rivero2024, 
author = {Jaicer López-Rivero and Hugo Cruz-Suárez and Carlos Camilo-Garay},
title = {Nash equilibria in risk-sensitive Markov stopping games under communication conditions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {23997-24017},
keywords = {Markov stopping games, risk-sensitive total expected reward, hitting time, certainty equivalent, birth-and-death chains},
url = {https://www.sciopen.com/article/10.3934/math.20241167},
doi = {10.3934/math.20241167},
abstract = {This paper analyzes the existence of Nash equilibrium in a discrete-time Markov stopping game with two players. At each decision point, Player Ⅱ is faced with the choice of either ending the game and thus granting Player Ⅰ a final reward or letting the game continue. In the latter case, Player Ⅰ performs an action that affects transitions and receives a running reward from Player Ⅱ. We assume that Player Ⅰ has a constant and non-zero risk sensitivity coefficient, while Player Ⅱ strives to minimize the utility of Player Ⅰ. The effectiveness of decision strategies was measured by the risk-sensitive expected total reward of Player Ⅰ. Exploiting mild continuity-compactness conditions and communication-ergodicity properties, we found that the value function of the game is described as a single fixed point of the equilibrium operator, determining a Nash equilibrium. In addition, we provide an illustrative example in which our assumptions hold.}
}