A mechanism implements a social choice correspondence f in mixed Nash equilibrium if at any preference profile, the set of all pure and mixed Nash equilibriumoutcomes coincides with the set of f-optimal alternatives at that preference profile. This definition generalizes Maskin’s definition of...

Theoretical models of multi-unit, uniform-price auctions assume that the price is given by the highest losing bid. In practice, however, the price is usually given by the lowest winning bid. We derive the equilibrium bidding function of the lowest-winning-bid auction when there are k objects for...