Quantum Communication Complexity of Classical Auctions

2023-11-21

arXiv.org

AI Summary

This work investigates the efficiency advantage of quantum communication over classical communication in Bayesian revenue-maximizing auctions, focusing on communication complexity in single-buyer, multi-item settings. Method: Integrating quantum communication protocols, information-theoretic analysis, game-theoretic modeling, and lower-bound proofs for communication complexity, the study systematically analyzes strategic mechanism design under quantum information constraints. Contribution/Results: The paper establishes the first quantum-classical separation in strategic mechanism design: (i) exponential communication compression in unit-demand and combinatorial valuation auctions; (ii) an exponential lower bound on the product of communication cost and payment precision; and (iii) three strict separations in two-item additive valuation settings—namely, infinite classical bits versus only 1 qubit + 2 classical bits; impossibility of one-way quantum protocols versus feasibility of minimal interactive quantum protocols; and failure of all finite quantum protocols. These results characterize the existence boundary of quantum-optimal auctions and affirm the distinct theoretical value of quantum communication in mechanism design.

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: 1. 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. 2. 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. 3. There exists a prior where no multi-round quantum auction protocol with a finite bound on communication complexity can obtain the optimal revenue.

Problem

• Quantum Communication
• Auction Theory
• Information Efficiency

Innovation

• Quantum Communication
• Information Efficiency
• Interactive Quantum Auctions