Separating the Communication Complexity of Truthful and Non-Truthful Combinatorial Auctions
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We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a (3/4-1/240+ε)-approximation for two buyers with XOS valuations over m items requires exp(Ω(ε^2 · m)) communication, whereas a non-truthful algorithm by Dobzinski and Schapira [SODA 2006] and Feige [2009] is already known to achieve a 3/4-approximation in poly(m) communication. We obtain our separation by proving that any simultaneous protocol (not necessarily truthful) which guarantees a (3/4-1/240+ε)-approximation requires communication exp(Ω(ε^2 · m)). The taxation complexity framework of Dobzinski [FOCS 2016] extends this lower bound to all truthful mechanisms (including interactive truthful mechanisms).
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