PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 27 | 3 | 251-263
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
27
Numer
3
Strony
251-263
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-09-17
poprawiono
1999-12-28
Twórcy
  • Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  • Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
  • [1] H. F. Bohnenblust, S. Karlin, and L. S. Shapley, Games with continuous, convex pay-off, in: H. W. Kuhn and A. W. Tucker (eds.), Contributions to the Theory of Games, I, Ann. of Math. Stud. 24, Princeton Univ. Press, Princeton, 1950, 181-192.
  • [2] R. Cowan and J. Zabczyk, An optimal selection problem associated with the Poisson process, Theory Probab. Appl. 23 (1978), 584-592.
  • [3] M. Dresher, The Mathematics of Games of Strategy, Dover, New York, 1981.
  • [4] E. G. Enns, Selecting the maximum of a sequence with imperfect information, J. Amer. Statist. Assoc. 70 (1975), 640-643.
  • [5] E. G. Enns and E. Ferenstein, The horse game, J. Oper. Res. Soc. Japan 28 (1985), 51-62.
  • [6] E. G. Enns and E. Ferenstein, On a multi-person time-sequential game with priorities, Sequential Anal. 6 (1987), 239-256.
  • [7] E. Z. Ferenstein, Two-person non-zero-sum sequential games with priorities, in: T. S. Ferguson and S. M. Samuels (eds.), Strategies for Sequential Search and Selection in Real Time (Amherst, MA, 1990), Contemp. Math. 125, Amer. Math. Soc. 1992, 119-133.
  • [8] T. S. Ferguson, Who solved the secretary problem?, Statist. Sci. 4 (1989), 282-296.
  • [9] P. R. Freeman, The secretary problem and its extensions: a review, Internat. Statist. Rev. 51 (1983), 189-206.
  • [10] A. A. K. Majumdar, Optimal stopping for a two-person sequential game in the continuous case, Pure Appl. Math. Sci. 22 (1985), 79-89.
  • [11] A. A. K. Majumdar, Optimal stopping for a two-person sequential game in the discrete case, ibid. (1986), 67-75.
  • [12] P. Neumann, Z. Porosiński and K. Szajowski, On two person full-information best choice problems with imperfect observation, Nova J. Math. Game Theory Algebra 5 (1996), 357-365.
  • [13] T. Parthasarathy and T. E. S. Raghavan, Equilibria of continuous two-person games, Pacific J. Math. 57 (1975), 265-270.
  • [14] Z. Porosiński, Full-information best choice problems with imperfect observation and a random number of observations, Zastos. Mat. 21 (1991), 179-192.
  • [15] E. L. Presman and I. M. Sonin, The best choice problem for a random number of objects, Theory Probab. Appl. 18 (1972), 657-592.
  • [16] T. Radzik, Nash equilibria of discontinuous non-zero-sum two-person games, Internat. J. Game Theory 21 (1993), 429-437.
  • [17] T. Radzik and K. Szajowski, Sequential games with random priority, Sequential Anal. 9 (1990), 361-377.
  • [18] G. Ravindran and K. Szajowski, Non-zero sum game with priority as Dynkin's game, Math. Japon. 37 (1992), 401-413.
  • [19] J. S. Rose, Twenty years of secretary problems: a survey of developments in the theory of optimal choice, Management Stud. 1 (1982), 53-64.
  • [20] M. Sakaguchi, A note on the dowry problem, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs. 20 (1973), 11-17.
  • [21] M. Sakaguchi, Non-zero-sum games related to the secretary problem, J. Oper. Res. Soc. Japan 23 (1980), 287-293.
  • [22] M. Sakaguchi, Best choice problems with full information and imperfect observation, Math. Japon. 29 (1984), 241-250.
  • [23] M. Sakaguchi, Bilateral sequential games related to the no-information secretary problem, ibid. 29 (1984), 961-974.
  • [24] M. Sakaguchi, Some two-person bilateral games in the generalized secretary problem, ibid. 33 (1988), 637-654.
  • [25] K. Szajowski, On non-zero sum game with priority in the secretary problem, ibid. 37 (1992), 415-426.
  • [26] K. Szajowski, Double stopping by two decision makers, Adv. Appl. Probab. 25 (1993), 438-452.
  • [27] K. Szajowski, Markov stopping games with random priority, Z. Oper. Res. 37 (1993), 69-84.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i3p251bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.