Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items

Kazuo Murota; Akiyoshi Shioura; Zaifu Yang

doi:10.1007/978-3-642-45030-3_44

Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items

Kazuo Murota, Akiyoshi Shioura, Zaifu Yang

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Citations (Scopus)

Abstract

We address the problem of computing a Walrasian equilibrium price in an ascending auction with gross substitutes valuations. In particular, an auction market is considered where there are multiple differentiated items and each item may have multiple units. Although the ascending auction is known to find an equilibrium price vector in finite time, little is known about its time complexity. The main aim of this paper is to analyze the time complexity of the ascending auction globally and locally, by utilizing the theory of discrete convex analysis. An exact bound on the number of iterations is given in terms of the ℓ_∞ distance between the initial price vector and an equilibrium, and an efficient algorithm to update a price vector is designedbased on a min-max theorem for submodular function minimization.

Original language	English
Title of host publication	Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings
Pages	468-478
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-45030-3_44
Publication status	Published - 2013
Event	24th International Symposium on Algorithms and Computation, ISAAC 2013 - Hong Kong, China Duration: 2013 Dec 16 → 2013 Dec 18

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8283 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	24th International Symposium on Algorithms and Computation, ISAAC 2013
Country	China
City	Hong Kong
Period	13/12/16 → 13/12/18

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-45030-3_44

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Murota, K., Shioura, A., & Yang, Z. (2013). Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. In Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings (pp. 468-478). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS). https://doi.org/10.1007/978-3-642-45030-3_44

Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. / Murota, Kazuo; Shioura, Akiyoshi; Yang, Zaifu.

Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. 2013. p. 468-478 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8283 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Murota, K, Shioura, A & Yang, Z 2013, Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. in Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8283 LNCS, pp. 468-478, 24th International Symposium on Algorithms and Computation, ISAAC 2013, Hong Kong, China, 13/12/16. https://doi.org/10.1007/978-3-642-45030-3_44

Murota K, Shioura A, Yang Z. Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. In Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. 2013. p. 468-478. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-45030-3_44

Murota, Kazuo ; Shioura, Akiyoshi ; Yang, Zaifu. / Computing a Walrasian equilibrium in iterative auctions with multiple differentiated items. Algorithms and Computation - 24th International Symposium, ISAAC 2013, Proceedings. 2013. pp. 468-478 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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