Settling the Communication Complexity of Combinatorial Auctions with Two Subadditive Buyers

We study the communication complexity of welfare maximization in combinatorial auctions with m items and two players with subadditive valuations. We show that outperforming the trivial 1/2-approximation requires exponential communication, settling an open problem of Dobzinski, Nisan and Schapira [STOC’05, MOR’10] and Feige [STOC’06, SICOMP ’09]. To derive our results, we introduce a new class of subadditive functions that are “far from” fractionally subadditive (XOS) functions, and establish randomized communication lower bounds for a new “near-EQUALITY” problem, both of which may be of independent interest.