The Complexity and Algorithm for k-Duplicates Combinatorial Auctions with Submodular and Subadditive Bidders

In this paper, we study the problem of maximizing welfare in combinatorial auctions with k(> 1)duplicates of each item, where k is a fixed constant (i.e. k is not the part of the input) and bidders are submodular or subadditive. We exhibit some upper and lower approximation bounds for k-duplicates combinatorial auctions. First, we show that it is NP-hard to approximate the maximum welfare for k-duplicates combinatorial auctions with subadditive bidders within a factor of 2− where > 0 unless P = NP . Secondly, we propose a 2-approximation algorithm for kduplicates combinatorial auctions with submodular bidders.