Incentive compatible multi unit combinatorial auctions

Abstract

School of C o m p u t e r Science a n d Engineering, H e b r e w University, J e r u s a l e m 91904, Israel A b s t r a c t This paper deals with multi-unit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both on-line and off-line scenarios. This is the first result where non-VCG mechanisms are derived for non-single minded bidders for a natural model of combinatorial auctions.

Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders

“…Surprisingly, this is one of the only two incentive compatible approximation algorithms known for combinatorial auctions, that do not apply only to very restricted "single-parameter" domains. The second algorithm is described in [2].…”

“…However, these non-feasible solutions are only a logarithmic factor away from feasibility. For general valuations this does not help, but this is the reason that the k-duplicate version of combinatorial auctions can be well approximated [6,2,1].…”

A Lower Bound of 1 + φ for Truthful Scheduling Mechanisms

“…Related is also some work which has been done in the context of combinatorial auctions which is a generalization of the scheduling problem (see for example [3,6,7,10,5,11] and the references within). Saks and Yu [25] proved that for convex domains the Monotonicity Property characterizes the class of social choice functions implementable by truthful mechanisms, generalizing results of [14,19].…”

Auctions, Bidding and Exchange Design

“…The optimal winner-determination problem remains intractable, even in this single-minded setting. Bartal et al [BGN03] have proposed a truthful and feasible mechanism for the multi-unit combinatorial allocation problem, in which each bidder is restricted to demand a small fraction of the available units of each good.…”