Separating the communication complexity of truthful and non-truthful combinatorial auctions

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] andFeige [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).