Volume

Dagstuhl Seminar Proceedings, Volume 10171

Publication Details

  • published at: 2010-07-15
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.10171.1
10171 Abstracts Collection – Equilibrium Computation

Authors: Edith Elkind, Nimrod Megiddo, Peter Bro Miltersen, Bernhard von Stengel, and Vijay V. Vazirani

Abstract
From April 25 to April 30, 2010, the Dagstuhl Seminar 10171 ``Equilibrium Computation'' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Edith Elkind, Nimrod Megiddo, Peter Bro Miltersen, Bernhard von Stengel, and Vijay V. Vazirani. 10171 Abstracts Collection – Equilibrium Computation. In Equilibrium Computation. Dagstuhl Seminar Proceedings, Volume 10171, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{elkind_et_al:DagSemProc.10171.1,
  author =	{Elkind, Edith and Megiddo, Nimrod and Miltersen, Peter Bro and von Stengel, Bernhard and Vazirani, Vijay V.},
  title =	{{10171 Abstracts Collection – Equilibrium Computation}},
  booktitle =	{Equilibrium Computation},
  pages =	{1--18},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10171},
  editor =	{Edith Elkind and Nimrod Megiddo and Peter Bro Miltersen and Vijay V. Vazirani and Bernahrd von Stengel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10171.1},
  URN =		{urn:nbn:de:0030-drops-26738},
  doi =		{10.4230/DagSemProc.10171.1},
  annote =	{Keywords: Equilibrium computation, algorithmic game theory}
}
Document
DOI: 10.4230/DagSemProc.10171.2
Improved Algorithms for Computing Fisher's Market Clearing Prices

Authors: James B. Orlin

Abstract
We give the first strongly polynomial time algorithm for computing an equilibrium for the linear utilities case of Fisher's market model. We consider a problem with a set $B$ of buyers and a set $G$ of divisible goods. Each buyer $i$ starts with an initial integral allocation $e_i$ of money. The integral utility for buyer $i$ of good $j$ is $U_{ij}$. We first develop a weakly polynomial time algorithm that runs in $O(n^4 log U_{max} + n^3 e_{max})$ time, where $n = |B| + |G|$. We further modify the algorithm so that it runs in $O(n^4 log n)$ time. These algorithms improve upon the previous best running time of $O(n^8 log U_{max} + n^7 log e_{max})$, due to Devanur et al.
Cite as

James B. Orlin. Improved Algorithms for Computing Fisher's Market Clearing Prices. In Equilibrium Computation. Dagstuhl Seminar Proceedings, Volume 10171, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{orlin:DagSemProc.10171.2,
  author =	{Orlin, James B.},
  title =	{{Improved Algorithms for Computing Fisher's Market Clearing Prices}},
  booktitle =	{Equilibrium Computation},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10171},
  editor =	{Edith Elkind and Nimrod Megiddo and Peter Bro Miltersen and Vijay V. Vazirani and Bernahrd von Stengel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10171.2},
  URN =		{urn:nbn:de:0030-drops-26720},
  doi =		{10.4230/DagSemProc.10171.2},
  annote =	{Keywords: Market equilibrium, Fisher, strongly polynomial}
}
Document
DOI: 10.4230/DagSemProc.10171.3
Proportional Response as Iterated Cobb-Douglas

Authors: Michael J. Todd

Abstract
We show that the proportional response algorithm for computing an economic equilibrium in a Fisher market model can be interpreted as iteratively approximating the economy by one with Cobb-Douglas utilities, for which a closed-form equilibrium can be obtained. We also extend the method to allow elasticities of substitution at most one.
Cite as

Michael J. Todd. Proportional Response as Iterated Cobb-Douglas. In Equilibrium Computation. Dagstuhl Seminar Proceedings, Volume 10171, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{todd:DagSemProc.10171.3,
  author =	{Todd, Michael J.},
  title =	{{Proportional Response as Iterated Cobb-Douglas}},
  booktitle =	{Equilibrium Computation},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10171},
  editor =	{Edith Elkind and Nimrod Megiddo and Peter Bro Miltersen and Vijay V. Vazirani and Bernahrd von Stengel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10171.3},
  URN =		{urn:nbn:de:0030-drops-26713},
  doi =		{10.4230/DagSemProc.10171.3},
  annote =	{Keywords: Computing equilibria, Fisher market, proportional response algorithm, Cobb-Douglas utilities}
}

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  • Authors
  • E
  • Elkind, Edith
  • M
  • Megiddo, Nimrod
  • Miltersen, Peter Bro
  • O
  • Orlin, James B.
  • T
  • Todd, Michael J.
  • V
  • Vazirani, Vijay V.
  • von Stengel, Bernhard

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