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Guess the Larger Number

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PL
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Języki publikacji
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Abstrakty
EN
We discuss variations of the zero-sum game where Bob selects two distinct numbers, and Alice learns one of them to make a guess which of the numbers is the larger.
PL
Przedmiotem rozważań są odmiany gry o sumie zerowej, gdy Bob wybiera dwa różne numery, a Alice dowiaduje się jedną z nich, by zgadnąć, która z liczb jest większa.
Rocznik
Strony
183–--207
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Queen Mary University of London, School of Mathematical Sciences, Mile End Road, London E1 4NS, U.K.
Bibliografia
  • [1] B. Berezovsky and A. Gnedin, The best choice problem, Moscow, Nauka, 1984. MR 0768372.
  • [2] D. Blackwell (1951), On the translation parameter problem for discrete variables, Annals of Mathematical Statistics 22: 391–399. doi: 10.1214/aoms/1177729585; MR 0043418.
  • [3] D. Blackwell and M. A. Girshick, Theory of games and statistical decisions, Dover, N.Y., 1979.
  • [4] F. T. Bruss (1996), The fallacy of the two-envelopes problem, Mathematical Scientist 21: 112–119.
  • [5] F. T. Bruss (2003), Playing a trick on uncertainty, Newsletter of the European Mathematical Society, issue 50, pp. 5 and 7-8 (online).
  • [6] G. Campbell and S. M. Samuels (1981), Choosing the best of the current crop, Advances in Applied Probability 13: 510–532. MR 0615949.
  • [7] Y. S. Chow and H. Teicher, Probability theory: Independence, interchangeability, martingales, Springer Texts in Statistics, Springer, New York, 1997. doi: 10.1007/978-1-4612-1950-7; MR 1476912.
  • [8] T. Cover (1987), Pick the largest number, In: Open Problems in Communication and Computation, T. Cover and B. Gopinath eds, Springer, p. 152. doi: 10. 10071/ 978-1-4612-4808-8.
  • [9] L. Devroye, Non-uniform random variate generation, Springer-Verlag, New York, 1986. doi: 10.1007/978-1-4613-8643-8; MR 836973.
  • [10] T. Ferguson (1989), Who solved the secretary problem? Statistical Science 4: 282–289. MR 1015277.
  • [11] A. Gnedin (1994), A solution to the game of googol, Annals of Probability 22: 1588–1595. MR 1303655.
  • [12] A. Gnedin (1996), Das Spiel Googol, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II. MR 1422387.
  • [13] A. Gnedin (1995), On a class of exchangeable sequences, Statistics and Probability Letters 25: 351-356. MR 1363235.
  • [14] A. Gnedin and U. Krengel (1995), A stochastic game of optimal stopping and order selection, Annals of Applied Probability 5: 310–321. MR 1325055.
  • [15] A. Gnedin and U. Krengel (1996), Optimal selection problems based on exchangeable trials, Annals of Applied Probability 6: 862–882. MR 1410118.
  • [16] A. Gnedin and G. Olshanski (2012), The two-sided infinite extension of the Mallows model for random permutations, Advances in Applied Mathematics 48: 615-639. MR 2920835.
  • [17] B. M. Hill (1968), Posterior distribution of percentiles: Bayes’ theorem for sampling from a population, Journal of the American Statistical Association 63: 677–691. MR 0238430.
  • [18] T. P. Hill (2009), Knowing when to stop, American Scientist 97, No. 2 (online).
  • [19] T. P. Hill and U. Krengel (1992), On the game of googol, International Journal of Game Theory 21: 151–160. MR 1203008.
  • [20] H. P. Kirschner (1976), On the risk-equivalence of two methods of randomization in statistics, Journal of Multivariate Analysis 6: 159-166.
  • [21] D. A. Lane and W. D. Sudderth (1978), Diffuse models for sampling and predictive inference, Annals of Statistics 6: 1318–1336. MR 0523766.
  • [22] T. M. Liggett, Interacting particle systems, Springer, 2005.
  • [23] I. Molchanov, Theory of random sets, Springer, 2005.
  • [24] J. Petruccelli (1980), On a best choice problem with partial information, Annals of Statistics 8: 1171–1174. MR 585717.
  • [25] D. Samet, I. Samet and D. Schmeidler (2004), One observation behind two-envelope problems, American Mathematical Monthly 111: 347–351. MR 2057189.
  • [26] S. M. Samuels (1989), Who will solve the secretary problem? [Comment on Ferguson] Statistical Science 4: 289–291.
  • [27] S. M. Samuels, Secretary problems, In: Handbook of Sequential Analysis, B. K. Ghosh and P. K. Sen eds, Marcel Dekker, NY, 1991. ISBN: 0-8247-8408-1; MR 1174296.
  • [28] S. Sorin, A first course on zero-sum repeated games, Springer, 2002.
  • [29] T. J. Stewart (1978), Optimal selection from a random sequence with learning of the underlying distribution, Journal of the American Statistical Association, 73: 775–780. MR 0521326.
  • [30] K. Szajowski (1984), Optimal stopping of a sequence of maxima over an unobservable sequence of maxima, Applicationes Mathematicae 18: 359–374. MR 0757886.
  • [31] P. Winkler (2001), Games people don’t play, In: Puzzlers Tribute: A Feast for the Mind, D. Wolfe and T. Rodgers eds., AK Peters. ISBN10 : 1-56881121-7.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
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