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Powers, Michael R.
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 3 [Year:] 2015 [Issue:] 1 [Pages:] 26-34
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.
two-envelope paradox
dominance reasoning
von Neumann-Morgenstern utility
heavy-tailed payoffs
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