2020/11/14 by Sepehr Assadi, Assadi, Sepehr, Hrishikesh Khandeparkar +5 · 1 citation
Computer Science · #Computational Complexity (cs.CC) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #cs.CC #cs.GT
paper · pdf · doi:10.48550/arxiv.2011.07414
arxiv created 2020/11/14 · arxiv updated 2020/11/17
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(ε2 ⋅ 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(ε2 ⋅ m)). The taxation complexity framework of Dobzinski [FOCS 2016] extends this lower bound to all truthful mechanisms (including interactive truthful mechanisms).