On the complexity of equilibrium computation in first-price auctions

Filos-Ratsikas, A., Giannakopoulos, Y. , Hollender, A., Lazos, P. and Poças, D. (2023) On the complexity of equilibrium computation in first-price auctions. SIAM Journal on Computing, 52(1), pp. 80-131. (doi: 10.1137/21M1435823)

Abstract

We consider the problem of computing a (pure) Bayes–Nash equilibrium in the first-price auction with continuous value distributions and discrete bidding space. We prove that when bidders have independent subjective prior beliefs about the value distributions of the other bidders, computing an ε-equilibrium of the auction is PPAD-complete, and computing an exact equilibrium is FIXP-complete. We also provide an efficient algorithm for solving a special case of the problem for a fixed number of bidders and available bids.

• Item Type: Articles
• Additional Information: Funding: Part of this work was done while the second and fifth authors were members of the Operations Research group at Technical University of Munich, School of Management, supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). The third author was supported by an EPSRC doctoral studentship (reference 1892947). The fourth author was partially supported by the ERC Advanced Grant 788893 AMDROMA, “Algorithmic and Mechanism Design Research in Online Markets,” and MIUR PRIN project ALGADIMAR, “Algorithms, Games, and Digital Markets.” The fifth author was supported by FCT via LASIGE Research Unit, reference UIDB/00408/2020.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Giannakopoulos, Dr Yiannis
• Authors: Filos-Ratsikas, A., Giannakopoulos, Y., Hollender, A., Lazos, P., and Poças, D.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: SIAM Journal on Computing
• Publisher: Society for Industrial and Applied Mathematics
• ISSN: 0097-5397
• ISSN (Online): 1095-7111
• Published Online: 14 February 2023
• Copyright Holders: Copyright © by SIAM
• First Published: First published in SIAM Journal on Computing 52(1):80-131
• Publisher Policy: Reproduced in accordance with the publisher copyright policy