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Proposition 10. Let X = (X1, X2) be a two-good random valuation with independent goods (not necessarily weakly regular). Then ...
(Indeed, the proof of Proposition 10 does not use the weak regularity assumption for X; moreover, while for weakly regular goods the result is a trivial consequence of Theorem 9 [because MonRev is less or equal to Rev], for general goods it does not follow from Theorem 7.)