There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, the authors find it useful to study preferences over solutions in their own right. They identify a set of appealing axioms on such...

This note uses Farkas's Lemma to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite.