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

@article{Assadi2020SeparatingTC,
  title={Separating the communication complexity of truthful and non-truthful combinatorial auctions},
  author={Sepehr Assadi and Hrishikesh Khandeparkar and Raghuvansh R. Saxena and S. Matthew Weinberg},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  year={2020}
}
We prove the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful auction guaranteeing a (34−1240+є)-approximation for two buyers with XOS valuations over m items requires exp(Ω(ε2 · m)) communication whereas a non-truthful auction by Feige [J. Comput. 2009] is already known to achieve a 34-approximation in (m) communication. We obtain our lower bound for truthful… 
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