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

*Michael Powers* ()

*Risks*, 2015, vol. 3, issue 1, 1-9

**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.

**Keywords:** two-envelope paradox; dominance reasoning; von Neumann–Morgenstern utility; heavy-tailed payoffs; boundedness (search for similar items in EconPapers)

**JEL-codes:** C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)

**Date:** 2015

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**Persistent link:** https://EconPapers.repec.org/RePEc:gam:jrisks:v:3:y:2015:i:1:p:26-34:d:44877

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