Exponential communication inefficiency of demand queries

In the problem of …nding an e¢ cient allocation when agents’utilities are privately known, we examine the e¤ect of restricting attention to mechanisms using “demand queries,” which ask agents to report an optimal allocation given a price list. We construct a combinatorial allocation problem with m items and two agents whose valuations lie in a certain class, such that (i) e¢ ciency can be obtained with a mechanism using O (m) bits, but (ii) any demand-query mechanism guaranteeing a higher e¢ ciency than giving all items to one agent uses a number of queries that is exponential in m. The same is proven for any demand-query mechanism achieving an improvement in expected e¢ ciency, for a constructed joint probability distribution over agents’valuations from the class. These results cast doubt on the usefulness of such common combinatorial allocation mechanisms as “iterative auctions”and other “preference elicitation” mechanisms using demand queries, as well as “value queries” and “order queries” (which are easily replicated with demand queries in our setting).