Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 746-749
Citer cet article
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/
@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},
year = {1969},
volume = {14},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a16/}
}
TY - JOUR
AU - E. B. Frid
TI - The optimal stopping rule for a Markov chain controlled by two persons with contradictory interests
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1969
SP - 746
EP - 749
VL - 14
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a16/
LA - ru
ID - TVP_1969_14_4_a16
ER -
%0 Journal Article
%A E. B. Frid
%T The optimal stopping rule for a Markov chain controlled by two persons with contradictory interests
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1969
%P 746-749
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a16/
%G ru
%F TVP_1969_14_4_a16
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.
