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

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

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 ...

The Two-Envelope Paradox: An Axiomatic Approach

There has been much recent discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisb...

The Two-Envelope Paradox: A Complete Analysis?

March 22, 1994 A wealthy eccentric places two envelopes in front of you. She tells you that both envelopes contain money, and that one contains twice as much as the other, but she does not tell you which is which. You are allowed to choose one envelope, and to keep all the money you find inside. This may seem innocuous, but it generates an apparent paradox. Say that you choose envelope 1, and i...

The Two-Envelope Paradox, Nonstandard Expected Utility, and the Intensionality of Probability

You are given a choice between two envelopes. You are told, reliably, that each envelope has some money in it—some whole number of dollars, say—and that one envelope contains twice as much money as the other. You don’t know which has the higher amount and which has the lower. You choose one, but are given the opportunity to switch to the other. Here is an argument that it is rationally preferab...

Randomization and Heavy - Tailed Behavior in Proof