Combinatorial auctions are currently becoming a common practice in industrial procurement, allowing bidders (sellers of goods and services in the procurement setting) to avoid the risk of selling good or service bundles that are incomplete, inefficient, or excessively expensive to deliver. Two major concerns in combinatorial auction design are the revelation or discovery of market price informa...

Given a winning-bid withdrawal in a combinatorial auction, finding an alternative repair solution of adequate revenue without causing undue disturbance to the remaining winning bids in the original solution may be difficult or even impossible. This “bid-takers exposure problem” may be preemptively addressed by finding a solution that is robust to winning-bid withdrawal. We introduce the concept...

We study the recognized open problem of designing revenuemaximizing combinatorial auctions. It is unsolved even for two bidders and two items for sale. Rather than pursuing the pure economic approach of attempting to characterize the optimal auction, we explore techniques for automatically modifying existing mechanisms in a way that increase expected revenue. We introduce a general family of au...

We consider auctions in which greedy algorithms, paired with first-price or criticalprice payment rules, are used to resolve multiparameter combinatorial allocation problems. We study the price of anarchy for social welfare in such auctions. We show, for a variety of equilibrium concepts, including Bayes–Nash equilibria, low-regret bidding sequences, and asynchronous bestresponse dynamics, that...

This paper studies the possibility of implementing Pareto optimal outcomes in the combinatorial auction setting where bidders may have budget constraints. I show that when the setting involves a single good, or multiple goods but with single-minded bidders, there is a unique mechanism, called truncation VCG, that is individually rational, incentive compatible and Pareto optimal. Truncation VCG ...

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instan...

Combinatorial auctions provide a valuable mechanism for the allocation of goods in settings where buyer valuations exhibit complex structure with respect to substitutabilityand complementarity. Most algorithms are designed to work with explicit bids for concrete bundles of goods. However, logical bidding languages allow the expression of complex utility functions in a natural and concise way. W...

The bipartite matching problem and the closely related assignment problem form a cornerstone of the Networks literature. In this paper we consider the problem of a firm whose valuation function for bundles of goods is determined by an optimal assignment of goods among several agents (or tasks,) each with independent valuations for each good. Though this model of preferences may be useful on its...

In a combinational auction in which bidders can bid on any combination of goods, bid data can be of exponential size. We describe an innovative new combinatorial auction format in which bidders submit “matrix bids”. The advantage of this approach is that it provides bidders a mechanism to compactly express bids on every possible bundle. We describe many different types of preferences that can b...

We present a cryptographic protocol for conducting efficient, provably-correct and secrecy-preserving combinatorial clock-proxy auctions. The “clock phase” functions as a trusted auction despite price discovery: bidders submit encrypted bids, and prove for themselves that they meet activity rules, and can compute total demand and thus verify price increases without revealing any information abo...