Truth Revelation in Rapid, Approximately EÆcient Combinatorial Auctions

Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a diÆcult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms in particular, their truth revelation properties assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Speci cally, we look at a particular greedy optimization method, which has empirically been shown to perform well. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying suÆcient conditions for a combinatorial auction to be truth-revealing, conditions which have applicability beyond the speci c auction studied here. Permanent address: Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel This material is based upon work supported by DARPA's contractF30602-98-C-0214