Hard-to-Manipulate Combinatorial Auctions

Abstract

Mechanism design provides a framework to solve distributed optimization problems in systems of self-interested agents. The combinatorial auction is one such problem, in which there is a set of discrete items to allocate to agents. Unfortunately, recent results suggest that it is impossible to implement reasonable approximations without losing robustness to manipulation. Furthermore, the Vickrey-Clarke-Groves (VCG) mechanism is known to be vulnerable to manipulation when agents can bid under multiple false names. In this paper we relax incentive constraints and require only that useful manipulation be NP-hard. We prove that any tractable approximation algorithm can be made to produce a hard-to-manipulate (VCG-based) mechanism, providing a useful counterpoint to these negative results. We also show that falsename bid manipulation in the VCG is NP-hard.