This paper analyzes incentive compatible (truthful) mechanisms over restricted domains of preferences,. the leading example being combinatorial auctions. Our work generalizes the characterization of Roberts (1979) who showed that truthful mechanisms over unrestricted domains with at least 3 possible outcomes must be "affine maximizers". We show that truthful mechanisms for combinatorial auctions (and related restricted domains) must be "almost affine maximizers" if they also satisfy an additional requirement of "independence of irrelevant alternatives". This requirement is without loss of generality for unrestricted domains as well as for auctions between two players where all goods must be allocated. This implies unconditional results for these cases, including a new proof of Roberts' theorem. The computational implications of this characterization are severe, as reasonable "almost affine maximizers" are shown to be as computationally hard as exact optimization. This implies the near-helplessness of such truthful polynomial-time auctions in all cases where exact optimization is computationally intractable.
|Number of pages
|Annual Symposium on Foundations of Computer Science - Proceedings
|Published - 2003
|Proceedings: 44th Annual IEEE Symposium on Foundations of Computer Science - FOCS 2003 - Cambridge, MA, United States
Duration: 11 Oct 2003 → 14 Oct 2003