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...

We establish conditions under which an English auction for an indivisible risky asset has an efficient ex post equilibrium when the bidders are heterogeneous in both their exposures to, and their attitudes toward, the ensuing risk the asset will generate for the winning bidder. Each bidder's...