This note shows that if the space of events is sufficiently rich and the subjective probability function of each individual is non-atomic, then there is a sigma-algebra of events over which everyone will have the same probability function, and moreover, the range of these probabilities is the...

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.