We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the...

We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that...