# Random priority two-person full-information best choice problem with imperfect observation

• Volume: 27, Issue: 3, page 251-263
• ISSN: 1233-7234

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## Abstract

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The following version of the two-player best choice problem is considered. Two players observe a sequence of i.i.d. random variables with a known continuous distribution. The random variables cannot be perfectly observed. Each time a random variable is sampled, the sampler is only informed whether it is greater than or less than some level specified by him. The aim of the players is to choose the best observation in the sequence (the maximal one). Each player can accept at most one realization of the process. If both want to accept the same observation then a random assignment mechanism is used. The zero-sum game approach is adopted. The normal form of the game is derived. It is shown that in the fixed horizon case the game has a solution in pure strategies whereas in the random horizon case with a geometric number of observations one player has a pure strategy and the other one has a mixed strategy from two pure strategies. The asymptotic behaviour of the solution is also studied.

## How to cite

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Porosiński, Zdzisław, and Szajowski, Krzysztof. "Random priority two-person full-information best choice problem with imperfect observation." Applicationes Mathematicae 27.3 (2000): 251-263. <http://eudml.org/doc/219272>.

@article{Porosiński2000,
abstract = {The following version of the two-player best choice problem is considered. Two players observe a sequence of i.i.d. random variables with a known continuous distribution. The random variables cannot be perfectly observed. Each time a random variable is sampled, the sampler is only informed whether it is greater than or less than some level specified by him. The aim of the players is to choose the best observation in the sequence (the maximal one). Each player can accept at most one realization of the process. If both want to accept the same observation then a random assignment mechanism is used. The zero-sum game approach is adopted. The normal form of the game is derived. It is shown that in the fixed horizon case the game has a solution in pure strategies whereas in the random horizon case with a geometric number of observations one player has a pure strategy and the other one has a mixed strategy from two pure strategies. The asymptotic behaviour of the solution is also studied.},
author = {Porosiński, Zdzisław, Szajowski, Krzysztof},
journal = {Applicationes Mathematicae},
keywords = {mixed strategy; best choice problem; zero-sum game; stopping game},
language = {eng},
number = {3},
pages = {251-263},
title = {Random priority two-person full-information best choice problem with imperfect observation},
url = {http://eudml.org/doc/219272},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Porosiński, Zdzisław
AU - Szajowski, Krzysztof
TI - Random priority two-person full-information best choice problem with imperfect observation
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 3
SP - 251
EP - 263
AB - The following version of the two-player best choice problem is considered. Two players observe a sequence of i.i.d. random variables with a known continuous distribution. The random variables cannot be perfectly observed. Each time a random variable is sampled, the sampler is only informed whether it is greater than or less than some level specified by him. The aim of the players is to choose the best observation in the sequence (the maximal one). Each player can accept at most one realization of the process. If both want to accept the same observation then a random assignment mechanism is used. The zero-sum game approach is adopted. The normal form of the game is derived. It is shown that in the fixed horizon case the game has a solution in pure strategies whereas in the random horizon case with a geometric number of observations one player has a pure strategy and the other one has a mixed strategy from two pure strategies. The asymptotic behaviour of the solution is also studied.
LA - eng
KW - mixed strategy; best choice problem; zero-sum game; stopping game
UR - http://eudml.org/doc/219272
ER -

## References

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