Multi-Unit Pay-Your-Bid Auctions with Variable Awards

Abstract Multi-unit auctions in which bidders can win a variable number of units differ significantly from multi-unit auctions in which bidders can only win one unit. In an independent-private-values, pay-your-bid auction where bidders may win up to two units, we show that first-order conditions imply separating and pooling of bids must both occur with positive probability. This behavior is not found in multi-unit uniform-price auctions. It also contrasts with asymmetric first-price auctions of a single good, whose first-order conditions are superficially similar. A uniform-distribution example is analyzed numerically. Journal of Economic Literature Classification Numbers: D44, D82, C72.