We investigate the possibility of enhancing efficiency by awarding premiums to a set of highest bidders in an English auction - in a setting that extends Maskin and Riley (1984, Econometrica 52: 1473-1518) in three aspects: (i) the seller can be risk averse, (ii) the bidders can have...

This paper characterizes the optimal first-price auction (FPA) and second-price auction (SPA) for selling rights, contracts, or licenses that involve ensuing payoff uncertainty for the winning bidder. The distribution of the random payoff is common knowledge, except that bidders have private...