On the approximability of combinatorial exchange problems

Moshe Babaioff*, Patrick Briest, Piotr Krysta

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations

Abstract

In a combinatorial exchange the goal is to find a feasible trade between potential buyers and sellers requesting and offering bundles of indivisible goods. We investigate the approximability of several optimization objectives in this setting and show that the problems of surplus and trade volume maximization are inapproximable even with free disposal and even if each agent's bundle is of size at most 3. In light of the negative results for surplus maximization we consider the complementary goal of social cost minimization and present tight approximation results for this scenario. Considering the more general supply chain problem, in which each agent can be a seller and buyer simultaneously, we prove that social cost minimization remains inapproximable even with bundles of size 3, yet becomes polynomial time solvable for agents trading bundles of size 1 or 2. This yields a complete characterization of the approximability of supply chain and combinatorial exchange problems based on the size of traded bundles. We finally briefly address the problem of exchanges in strategic settings.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - First International Symposium, SAGT 2008, Proceedings
Pages83-94
Number of pages12
DOIs
StatePublished - 2008
Externally publishedYes
Event1st International Symposium on Algorithmic Game Theory, SAGT 2008 - Paderborn, Germany
Duration: 30 Apr 20082 May 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4997 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st International Symposium on Algorithmic Game Theory, SAGT 2008
Country/TerritoryGermany
CityPaderborn
Period30/04/082/05/08

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