Geodesic
The optimal stopping rule for a~Markov chain controlled by two persons with contradictory interests
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 746-749

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The paper considers a game described by a finite Markov chain with a state space $E$ subdivided into three disjoint subsets $E_1,E_2$ and $E_0$. The first player can stop the process on the set $E_1$ and the second one on the set $E_2$. The first player pays to the second player payment $g(x)$, if the process is stopped at the point $x$. The existence of the game value is proved and the optimal policies of the players are constructed. 
@article{TVP_1969_14_4_a16,
     author = {E. B. Frid},
     title = {The optimal stopping rule for {a~Markov} chain controlled by two persons with contradictory interests},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {746--749},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a16/}
}
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E. B. Frid. The optimal stopping rule for a~Markov chain controlled by two persons with contradictory interests. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 746-749. http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a16/