Communication Separations for Truthful Auctions: Breaking the Two-Player Barrier
Shiri Ron, Clayton Thomas, S. Matthew Weinberg, Qianfan Zhang

TL;DR
This paper investigates the communication complexity of truthful combinatorial auctions with subadditive or single-minded valuations, revealing exponential communication requirements for certain approximation guarantees with three bidders, and highlighting a gap between truthful and non-truthful protocols.
Contribution
It establishes the first exponential lower bounds for truthful mechanisms with three bidders in this setting, extending the taxation complexity framework beyond previous two-bidder limitations.
Findings
Deterministic truthful mechanisms need exponential communication for 0.366-approximation with three bidders.
Non-truthful protocols can achieve 0.5-approximation with polynomial communication.
A gap exists between truthful and non-truthful auction protocols in this context.
Abstract
We study the communication complexity of truthful combinatorial auctions, and in particular the case where valuations are either subadditive or single-minded, which we denote with . We show that for three bidders with valuations in , any deterministic truthful mechanism that achieves at least a -approximation requires communication. In contrast, a natural extension of [Fei09] yields a non-truthful -communication protocol that achieves a -approximation, demonstrating a gap between the power of truthful mechanisms and non-truthful protocols for this problem. Our approach follows the taxation complexity framework laid out in [Dob16b], but applies this framework in a setting not encompassed by the techniques used in past work. In particular, the only successful prior…
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Taxonomy
TopicsLaw, Economics, and Judicial Systems · Auction Theory and Applications · Legal and Constitutional Studies
