IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v3y2015i1p26-34d44877.html
   My bibliography  Save this article

Paradox-Proof Utility Functions for Heavy-Tailed Payoffs: Two Instructive Two-Envelope Problems

Author

Listed:
  • Michael R. Powers

    () (Department of Finance, School of Economics and Management, and Schwarzman Scholars Program, Tsinghua University, Beijing 100084, China)

Abstract

We identify restrictions on a decision maker’s utility function that are both necessary and sufficient to preserve dominance reasoning in each of two versions of the Two-Envelope Paradox (TEP). For the classical TEP, the utility function must satisfy a certain recurrence inequality. For the St. Petersburg TEP, the utility function must be bounded above asymptotically by a power function, which can be tightened to a constant. By determining the weakest conditions for dominance reasoning to hold, the article settles an open question in the research literature. Remarkably, neither constant-bounded utility nor finite expected utility is necessary for resolving the classical TEP; instead, finite expected utility is both necessary and sufficient for resolving the St. Petersburg TEP.

Suggested Citation

  • Michael R. Powers, 2015. "Paradox-Proof Utility Functions for Heavy-Tailed Payoffs: Two Instructive Two-Envelope Problems," Risks, MDPI, Open Access Journal, vol. 3(1), pages 1-9, January.
  • Handle: RePEc:gam:jrisks:v:3:y:2015:i:1:p:26-34:d:44877
    as

    Download full text from publisher

    File URL: http://www.mdpi.com/2227-9091/3/1/26/pdf
    Download Restriction: no

    File URL: http://www.mdpi.com/2227-9091/3/1/26/
    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)

    More about this item

    Keywords

    two-envelope paradox; dominance reasoning; von Neumann–Morgenstern utility; heavy-tailed payoffs; boundedness;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

    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:gam:jrisks:v:3:y:2015:i:1:p:26-34:d:44877. 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: (XML Conversion Team). General contact details of provider: http://www.mdpi.com/ .

    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.