IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v29y1996i1p23-32.html
   My bibliography  Save this article

Prophet compared to gambler: additive inequalities for transforms of sequences of random variables

Author

Listed:
  • Boshuizen, Frans A.

Abstract

Additive comparisons are given between optimal expected gains of a prophet and a gambler. A gambler knows only the past and the present and a prophet is a player with complete foresight. The optimal expected gains are obtained by betting on differences of consecutive uniformly bounded random variables. For example, if the random variables are i.i.d. and [0,1]-valued, then the difference between the prophet and the gambler is at most n/16 for a game of length n, and the bound n/16 is the best possible.

Suggested Citation

  • Boshuizen, Frans A., 1996. "Prophet compared to gambler: additive inequalities for transforms of sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 29(1), pages 23-32, August.
    • Handle: RePEc:eee:stapro:v:29:y:1996:i:1:p:23-32
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(95)00151-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boshuizen, F. A., 1994. "Optimal Stopping-Related Inequalities for Iid Random Variables when the Future Is Discounted," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 115-131, July.
    2. MERTENS, Jean-François & ZAMIR, Shmuel, 1977. "The maximal variation of a bounded martingale," LIDAM Reprints CORE 309, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abraham Neyman, 2009. "The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information," Discussion Paper Series dp510, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Abraham Neyman, 2012. "The value of two-person zero-sum repeated games with incomplete information and uncertain duration," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 195-207, February.
    3. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
    4. Abraham Neyman, 2013. "The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information," Journal of Theoretical Probability, Springer, vol. 26(2), pages 557-567, June.
    5. Jeffrey Ely & Alexander Frankel & Emir Kamenica, 2015. "Suspense and Surprise," Journal of Political Economy, University of Chicago Press, vol. 123(1), pages 215-260.
    6. Fedor Sandomirskiy, 2018. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," Dynamic Games and Applications, Springer, vol. 8(1), pages 180-198, March.
    7. Fedor Sandomirskiy, 2014. "Repeated games of incomplete information with large sets of states," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 767-789, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:29:y:1996:i:1:p:23-32. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.