Jump to ContentJump to Main Navigation
Combinatorial Auctions$
Users without a subscription are not able to see the full content.

Peter Cramton, Yoav Shoham, and Richard Steinberg

Print publication date: 2005

Print ISBN-13: 9780262033428

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262033428.001.0001

Show Summary Details
Page of

PRINTED FROM MIT PRESS SCHOLARSHIP ONLINE (www.mitpress.universitypressscholarship.com). (c) Copyright The MIT Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in MITSO for personal use.date: 29 June 2022

From the Assignment Model to Combinatorial Auctions

From the Assignment Model to Combinatorial Auctions

Chapter:
(p.189) 8 From the Assignment Model to Combinatorial Auctions
Source:
Combinatorial Auctions
Author(s):

Sushil Bikhchandani

Joseph M. Ostroy

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262033428.003.0009

In this chapter, the connection between efficient auctions for multiple, indivisible items and the duality theory of linear programming is investigated. Vickrey auctions are the focus of this investigation as they are efficient auctions well known for their incentive properties. The chapter begins with a description of the basic results for the assignment model that concerns allocations with indivisibilities and defines the combinatorial auction model and pricing equilibria, which is an extension of Walrasian equilibrium. It further discusses an equivalence between the sealed-bid Vickrey auction and pricing equilibrium. The chapter emphasizes that various combinatorial ascending price auctions are incentive compatible if an MP pricing equilibrium is implemented by them. It also discusses the implementation of dual algorithms, the subgradient algorithm, and the primal dual algorithm for solving linear programming problems.

Keywords:   combinatorial auctions, linear programming, Vickrey auction, pricing equilibrium, Walrasian equilibrium, subgradient algorithm, primal dual algorithm

MIT Press Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs, and if you can't find the answer there, please contact us.