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This interpretation of the two envelopes problem appears in the first publications in which the paradox was introduced in its present-day form, Gardner (1989) and Nalebuff (1988).<ref>{{Cite journal|last1=Nalebuff|first1=Barry|date=Spring 1988|title=Puzzles: Cider in Your Ear, Continuing Dilemma, The Last Shall Be First, and More|journal = Journal of Economic Perspectives|volume = 2|issue=2|pages=149–156|doi = 10.1257/jep.2.2.149 }} and Gardner, Martin (1989) <i> Penrose Tiles to Trapdoor Ciphers: And the Return of Dr Matrix. </i> </ref>)
It is common in the more mathematical literature on the problem. It also applies to the modification of the problem (which seems to have started with Nalebuff) in which the owner of envelope A does actually look in his envelope before deciding whether or not to switch; though Nalebuff does also emphasize that there is no need to have the owner of envelope A look in his envelope. If he imagines looking in it, and if for any amount which he can imagine being in there, he has an argument to switch, then he will decide to switch anyway. Finally, this interpretation was also the core of earlier versions of the two envelopes problem (Littlewood's, Schrödinger's, and Kraitchik's switching paradoxes); see [[Two envelopes problem#History of the paradox|the concluding section, on history of TEP]].
This kind of interpretation is often called "Bayesian" because it assumes the writer is also incorporating a prior probability distribution of possible amounts of money in the two envelopes in the switching argument.
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