Welfare guarantees for combinatorial auctions with item bidding

We analyze the price of anarchy (POA) in a simple and practical non-truthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate second-price auctions. We first prove that under a standard "no overbidding" assumption, for every subadditive valuation profile, every pure Nash equilibrium has welfare at least 50% of optimal --- i.e., the POA is at most 2. For the incomplete information setting, we prove that the POA with respect to Bayes-Nash equilibria is strictly larger than 2 --- an unusual separation from the full-information model --- and is at most 2 ln m, where m is the number of goods.