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

Risks

Michael R. Powers¹ 

[1] Department of Finance, School of Economics and Management, and Schwarzman Scholars Program, Tsinghua University, Beijing 100084, China; E-Mail

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

DOI  :  10.3390/risks3010026

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.