Concave Generalized Flows with Applications to Market Equilibria

Laszlo A. Vegh

Papers from arXiv.org

Abstract: We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an epsilon-approximate solution in O(m(m+log n)log(MUm/epsilon)) arithmetic operations and value oracle queries, where M and U are upper bounds on simple parameters. This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg, Plotkin and Tardos, not using any cycle cancellations. We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately extends these market models to more general settings. We also obtain a combinatorial algorithm for nonsymmetric Arrow-Debreu Nash bargaining, settling an open question by Vazirani.

Date: 2011-09, Revised 2012-04
New Economics Papers: this item is included in nep-cmp
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/1109.3893 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1109.3893

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().