Seller-Determined Two-Attribute Reverse Auctions: The Case of Linear Utilities

Auctions have been used in the procurement of heterogeneous goods as well as services, produced and delivered after the auctions conclude. In these situations the standard quasi-linearity assumption is violated and the price and other attributes are interrelated. Linear utilities are one of the most common and easy to construct and use. It is shown that the simplest case, when the utilities are linear functions of two attributes the auction mechanism is inefficient and it does not maximize social welfare. Furthermore, even if the winning bid is an efficient solution, a win-win solution which dominates this bid may be possible. This can be achieved when a seller initiates post-auction negotiations. Sellers negotiate with the buyer to accept a configuration that is worse (than the winning one) for the buyer but is better for the seller.