PERSPECTIVES ON A PAIR OF ENVELOPES

The two envelopes problem has generated a significant number of public ations (I have benefitted from reading many of them, only some of whic h 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 m isconceptions concerning the problem. Within a countably additive prob ability framework, the problem illustrates a breakdown of dominance wi th respect to infinite partitions in circumstances of infinite expecte d utility. Within a probability framework that is only finitely additi ve, there are failures of dominance with respect to infinite partition s in circumstances of bounded utility with finitely many consequences (see the epilogue).