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

Zdzisław Porosiński; Krzysztof Szajowski

Applicationes Mathematicae (2000)

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

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topPorosiński, 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 -

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