Perspectives on a Pair of Envelopes

Theory and Decision 43 (3):253-277 (1997)
The two envelopes problem has generated a significant number of publications (I have benefitted from reading many of them, only some of which I cite; see the epilogue for a historical note). Part of my purpose here is to provide a review of previous results (with somewhat simpler demonstrations). In addition, I hope to clear up what I see as some misconceptions concerning the problem. Within a countably additive probability framework, the problem illustrates a breakdown of dominance with respect to infinite partitions in circumstances of infinite expected utility. Within a probability framework that is only finitely additive, there are failures of dominance with respect to infinite partitions in circumstances of bounded utility with finitely many consequences (see the epilogue)
Keywords Pair of envelopes  countable additivity  principle of dominance  finite additivity  infinite partitions
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DOI 10.1023/A:1004976227366
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Paul Syverson (2010). Opening Two Envelopes. Acta Analytica 25 (4):479-498.

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