Article

Market equilibrium for CES exchange economies: existence, multiplicity, and computation

Authors:

Bruno Codenotti,

Sriram Penumatcha,

Kasturi VaradarajanAuthors Info & Claims

FSTTCS '05: Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science

Pages 505 - 516

https://doi.org/10.1007/11590156_41

Published: 15 December 2005 Publication History

Abstract

We consider exchange economies where the traders' preferences are expressed in terms of the extensively used constant elasticity of substitution (CES) utility functions. We show that for any such economy it is possible to say in polynomial time whether an equilibrium exists.

We then describe a convex formulation of the equilibrium conditions, which leads to polynomial time algorithms for a wide range of the parameter defining the CES utility functions. This range includes instances that do not satisfy weak gross substitutability. As a byproduct of our work, we prove the uniqueness of equilibrium in an interesting setting where such a result was not known.

The range for which we do not obtain polynomial-time algorithms coincides with the range for which the economies admit multiple disconnected equilibria.

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Chen XPaparas DYannakakis M(2017)The Complexity of Non-Monotone MarketsJournal of the ACM10.1145/306481064:3(1-56)Online publication date: 16-Jun-2017
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Garg JMehta RVazirani VShmoys D(2014)Dichotomies in equilibrium computation, and complementary pivot algorithms for a new class of non-separable utility functionsProceedings of the forty-sixth annual ACM symposium on Theory of computing10.1145/2591796.2591863(525-534)Online publication date: 31-May-2014
https://dl.acm.org/doi/10.1145/2591796.2591863
Goel ANazerzadeh H(2014)Price-based protocols for fair resource allocationACM Transactions on Algorithms10.1145/255694910:2(1-14)Online publication date: 1-Feb-2014
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Published In

cover image Guide Proceedings

FSTTCS '05: Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science

December 2005

566 pages

ISBN:3540304959

Editors:
Sundar Sarukkai
National Institute of Advanced Studies, Indian Institute of Science Campus, Bangalore, India
,
Sandeep Sen
Department of Comp. Sc. & Engg., Indian Institute of Technology Delhi, New Delhi, India

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 December 2005

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Cited By

Chen XPaparas DYannakakis M(2017)The Complexity of Non-Monotone MarketsJournal of the ACM10.1145/306481064:3(1-56)Online publication date: 16-Jun-2017
https://dl.acm.org/doi/10.1145/3064810
Garg JMehta RVazirani VShmoys D(2014)Dichotomies in equilibrium computation, and complementary pivot algorithms for a new class of non-separable utility functionsProceedings of the forty-sixth annual ACM symposium on Theory of computing10.1145/2591796.2591863(525-534)Online publication date: 31-May-2014
https://dl.acm.org/doi/10.1145/2591796.2591863
Goel ANazerzadeh H(2014)Price-based protocols for fair resource allocationACM Transactions on Algorithms10.1145/255694910:2(1-14)Online publication date: 1-Feb-2014
https://dl.acm.org/doi/10.1145/2556949
Chen XPaparas DYannakakis MBoneh DRoughgarden TFeigenbaum J(2013)The complexity of non-monotone marketsProceedings of the forty-fifth annual ACM symposium on Theory of Computing10.1145/2488608.2488632(181-190)Online publication date: 1-Jun-2013
https://dl.acm.org/doi/10.1145/2488608.2488632
Cheung YCole RRastogi AFaltings BLeyton-Brown KIpeirotis P(2012)Tatonnement in ongoing markets of complementary goodsProceedings of the 13th ACM Conference on Electronic Commerce10.1145/2229012.2229039(337-354)Online publication date: 4-Jun-2012
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Chen XTeng S(2009)Spending Is Not Easier Than TradingProceedings of the 20th International Symposium on Algorithms and Computation10.1007/978-3-642-10631-6_66(647-656)Online publication date: 5-Dec-2009
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Goel ANazerzadeh HTeng S(2008)Price based protocols for fair resource allocationProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347207(1145-1153)Online publication date: 20-Jan-2008
https://dl.acm.org/doi/10.5555/1347082.1347207
Codenotti BMccune BPemmaraju SRaman RVaradarajan K(2008)An experimental study of different approaches to solve the market equilibrium problemACM Journal of Experimental Algorithmics10.1145/1227161.140229512(1-21)Online publication date: 29-Aug-2008
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Codenotti BSaberi AVaradarajan KYe Y(2008)The complexity of equilibriaTheoretical Computer Science10.1016/j.tcs.2008.08.007408:2-3(188-198)Online publication date: 20-Nov-2008
https://dl.acm.org/doi/10.1016/j.tcs.2008.08.007
McCune B(2007)Extending polynomial time computability to markets with demand correspondencesProceedings of the 3rd international conference on Internet and network economics10.5555/1781894.1781940(347-355)Online publication date: 12-Dec-2007
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