IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/0310004.html
   My bibliography  Save this paper

One Observation behind Two-Envelope Puzzles

Author

Listed:
  • Dov Samet
  • Iddo Samet
  • David Schmeidler

Abstract

In two famous and popular puzzles a participant is required to compare two numbers of which she is shown only one. In the first one there are two envelopes with money in them. The sum of money in one of the envelopes is twice as large as the other sum. An envelope is selected at random and handed to you. If the sum in this envelope is x, then the sum in the other one is (1/2)(2x) + (1/2)(0.5x) = 1.25x. Hence, you are better off switching to the other envelope no matter what sum you see, which is paradoxical. In the second puzzle two distinct numbers are written on two slips of paper. One of them is selected at random and you observe it. How can you guess, with probability greater than 1/2 of being correct, whether this number is the larger or the smaller? We show that there is one principle behind the two puzzles: The ranking of n random variables X1, ... , Xn cannot be independent of each of them, unless the ranking is fixed. Thus, unless there is nothing to be learned about the ranking, there must be at least one variable the observation of which conveys information about it.

Suggested Citation

  • Dov Samet & Iddo Samet & David Schmeidler, 2003. "One Observation behind Two-Envelope Puzzles," Game Theory and Information 0310004, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0310004
    Note: Type of Document - ; pages: 6 . A PowerPoint XP presentation is available at
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0310/0310004.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Nalebuff, Barry, 1989. "The Other Person's Envelope Is Always Greener," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 171-181, Winter.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lehrer, Ehud & Samet, Dov, 2011. "Agreeing to agree," Theoretical Economics, Econometric Society, vol. 6(2), May.

    More about this item

    Keywords

    two envelope paradox;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpga:0310004. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.