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Quantum Communication Complexity of Classical Auctions

Authors Aviad Rubinstein , Zixin Zhou

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Author Details

Aviad Rubinstein
  • Department of Computer Science, Stanford University, CA, USA
Zixin Zhou
  • Department of Computer Science, Stanford University, CA, USA

Funding

  • Rubinstein, Aviad: Supported by NSFCCF-1954927, and a David and Lucile Packard Fellowship.
  • Zhou, Zixin: Supported by NSFCCF-1954927, and the Stanford interdisciplinary graduate fellowship.

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Aviad Rubinstein and Zixin Zhou. Quantum Communication Complexity of Classical Auctions. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 84:1-84:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.84

Abstract

We study the fundamental, classical mechanism design problem of single-buyer multi-item Bayesian revenue-maximizing auctions under the lens of communication complexity between the buyer and the seller. Specifically, we ask whether using quantum communication can be more efficient than classical communication. We have two sets of results, revealing a surprisingly rich landscape - which looks quite different from both quantum communication in non-strategic parties, and classical communication in mechanism design.
We first study the expected communication complexity of approximately optimal auctions. We give quantum auction protocols for buyers with unit-demand or combinatorial valuations that obtain an arbitrarily good approximation of the optimal revenue while running in exponentially more efficient communication compared to classical approximately optimal auctions. However, these auctions come with the caveat that they may require the seller to charge exponentially large payments from a deviating buyer. We show that this caveat is necessary - we give an exponential lower bound on the product of the expected quantum communication and the maximum payment.
We then study the worst-case communication complexity of exactly optimal auctions in an extremely simple setting: additive buyer’s valuations over two items. We show the following separations:  
- There exists a prior where the optimal classical auction protocol requires infinitely many bits, but a one-way message of 1 qubit and 2 classical bits suffices. 
- There exists a prior where no finite one-way quantum auction protocol can obtain the optimal revenue. However, there is a barely-interactive revenue-optimal quantum auction protocol with the following simple structure: the seller prepares a pair of qubits in the EPR state, sends one of them to the buyer, and then the buyer sends 1 qubit and 2 classical bits. 
- There exists a prior where no multi-round quantum auction protocol with a finite bound on communication complexity can obtain the optimal revenue.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Communication complexity
  • Theory of computation → Quantum computation theory
Keywords
  • Mechanism design
  • Communication complexity
  • Quantum computing

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