A Simple Ascending Generalized Vickrey Auction∗

We design a simple ascending Vickrey auction for the combinatorial allocation problem. We make use of a concept called universal competitive equilibrium (UCE) price to design our auction. Our auction searches for a UCE price, which (along with an efficient allocation) provides enough information to compute the Vickrey payments of buyers. Our auction maintains non-linear and non-anonymous prices. At every iteration, we identify the set of “unsatisfied” buyers in either the main economy or in one of the “marginal” economies and increase prices of the bundles demanded by these buyers. The auction terminates at a UCE price when there are no unsatisfied buyers in either the main economy or in any of the marginal economies. When buyers are substitutes, considering unsatisfied buyers from the main economy alone terminates the auction at a UCE price. Truthful bidding is an ex post Nash equilibrium for buyers in our auction. In a variant of this auction, we introduce dynamic price discrimination, thus maintaining anonymous prices in the auction as long as possible. This becomes a true generalization of the English auction to the combinatorial allocation problem.