Two Randomized Mechanisms for Combinatorial Auctions

This paper discusses two advancements in the theory of designing truthful randomized mechanisms. Our first contribution is a new framework for developing truthful randomized mechanisms. The framework enables the construction of mechanisms with polynomially small failure probability. This is in contrast to previous mechanisms that fail with constant probability. Another appealing feature of the new framework is that bidding truthfully is a stronglydominant strategy. The power of the framework is demonstrated by an $O(\sqrt m)$-mechanism for combinatorial auctions that succeeds with probability $1-O(\frac {\log m} {\sqrt m})$. The other major result of this paper is an O(logmloglogm) randomized truthful mechanism for combinatorial auction with subadditivebidders. The best previously-known truthful mechanism for this setting guaranteed an approximation ratio of $O(\sqrt m)$. En route, the new mechanism also provides the best approximation ratio for combinatorial auctions with submodularbidders currently achieved by truthful mechanisms.