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

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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 
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     author = {Cavazos-Cadena, Rolando and Hern\'andez-Hern\'andez, Daniel},
     title = {Nash {Equilibria} in a class of {Markov} stopping games},
     journal = {Kybernetika},
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     year = {2012},
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     language = {en},
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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/