Asymmetric English Auctions Revisited

I introduce a property of player's valuations that ensures the existence of an ex post efficient equilibrium in asymmetric English auctions. The use of this property has the advantage of yielding an ex post efficient equilibrium without assuming differentiability of valuations or that signals are drawn from a density. These technical, non economic, assumptions have been ubiquitous in the study of (potentially) asymmetric English auctions. Therefore, my work highlights the economic content of what it takes to obtain efficient ex post equilibria. I generalize prior work by Echenique and Manelli (2006) and by Birulin and Izmalkov (2003). Relative to Krishna (2003), I weaken his single crossing properties, drop his differentiability and densities assumptions, but I assume that one player's valuation is weakly increasing in other players' signals, while he uses a different assumption (neither stronger nor weaker)