One Observation behind Two-Envelope Puzzles

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One Observation behind Two-Envelope Puzzles

Author Info

Dov Samet
Iddo Samet
David Schmeidler

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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.

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Paper provided by EconWPA in its series Game Theory and Information with number 0310004.

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Length: 6 pages
Date of creation: 08 Oct 2003
Date of revision:
Handle: RePEc:wpa:wuwpga:0310004

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D8 - Microeconomics - - Information, Knowledge, and Uncertainty

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-10-12 (All new papers)
NEP-GTH-2003-10-12 (Game Theory)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Nalebuff, Barry, 1989. "The Other Person's Envelope Is Always Greener," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 171-81, Winter. [Downloadable!] (restricted)
Brams, Steven J. & Kilgour, D. Marc, 1990. "The Box Problem: To Switch Or Not To Switch?," Working Papers 90-26, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Ehud Lehrer & Dov Samet, 2003. "Agreeing to agree," Game Theory and Information 0310005, EconWPA. [Downloadable!]

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