Paradox-proof utility functions for heavy-tailed payoffs: Two instructive two-envelope problems

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Risks ; ISSN: 2227-9091 ; Volume: 3 ; Year: 2015 ; Issue: 1 ; Pages: 26-34 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft
• Subject: two-envelope paradox ; dominance reasoning ; von Neumann-Morgenstern utility ; heavy-tailed payoffs ; boundedness

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Powers, Michael R.
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2015

Further information

• DOI: doi:10.3390/risks3010026
• Handle: http://hdl.handle.net/10419/167837
• Last update: 10.03.2025, 11:45 AM CET