An Algorithm for Optimal Winner Determination in Combinatorial Auctions

Abstract

Combinatorial auctions, i.e. auctions where bidders can bid on combinations of items, tend to lead to more efficient allocations than traditional auctions in multi-item auctions where the agents' valuations of the items are not additive. However, determining the winners so as to maximize revenue is NP-complete. First, existing approaches for tackling this problem are reviewed: exhaustive enumeration, dynamic programming, approximation algorithms, and restricting the alloable combinations. Then we present our search algorithm for optimal winner determination. Experiments are shown on several bid distributions. The algorithm allows combinatorial auctions to scale up to significantly larger numbers of items and bids than prior approaches to optimal winner determination by capitalizing on the fact that the space of bids is necessarily sparsely populated in practice. The algorithm does this by provably sufficient selective generation of children in the search tree, by using a secondary search for fast child generation, by heuristics that are accurate and optimized for speed, and by four methods for preprocessing the search space.