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Author Vazirani, Vijay V. ♦ Yannakakis, Mihalis
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2011
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Arrow--Debreu market ♦ Fisher market ♦ Market equilibria ♦ PPAD ♦ Piecewise-linear utilities
Abstract We consider Fisher and Arrow--Debreu markets under additively separable, piecewise-linear, concave utility functions and obtain the following results. For both market models, if an equilibrium exists, there is one that is rational and can be written using polynomially many bits. There is no simple necessary and sufficient condition for the existence of an equilibrium: The problem of checking for existence of an equilibrium is NP-complete for both market models; the same holds for existence of an ε-approximate equilibrium, for ε = $O(n^{™5}).$ Under standard (mild) sufficient conditions, the problem of finding an exact equilibrium is in PPAD for both market models. Finally, building on the techniques of Chen et al. [2009a] we prove that under these sufficient conditions, finding an equilibrium for Fisher markets is PPAD-hard.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2011-06-09
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 58
Issue Number 3
Page Count 25
Starting Page 1
Ending Page 25

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Source: ACM Digital Library