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Limitations of Deterministic Auction Design for Correlated Bidders

Caragiannis, Ioannis and Kaklamanis, Christos and Kyropoulou, Maria (2016) 'Limitations of Deterministic Auction Design for Correlated Bidders.' ACM Transactions on Computation Theory, 8 (4). ISSN 1942-3454

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Abstract

The seminal work of Myerson (Mathematics of OR ’81) characterizes incentive-compatible single-item auctions among bidders with independent valuations. In this setting, relatively simple deterministic auction mechanisms achieve revenue optimality. When bidders have correlated valuations, designing the revenue-optimal deterministic auction is a computationally demanding problem; indeed, Papadimitriou and Pierrakos (STOC ’11) proved that it is APX-hard, obtaining an explicit inapproximability factor of 1999/2000 = 99.95%. In the current paper, we strengthen this inapproximability factor to 63/64 ≈ 98.5%. Our proof is based on a gap-preserving reduction from the Max-NM 3SAT problem; a variant of the maximum satisfiability problem where each clause has exactly 3 literals and no clause contains both negated and unnegated literals. We furthermore show that the gap between the revenue of deterministic and randomized auctions can be as low as 13/14 ≈ 92.9%, improving an explicit gap of 947/948 ≈ 99.9% by Dobzinski, Fu, and Kleinberg (STOC ’11).

Item Type: Article
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Elements
Date Deposited: 18 Dec 2018 13:29
Last Modified: 18 Dec 2018 13:29
URI: http://repository.essex.ac.uk/id/eprint/23659

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