### Market equilibrium under separable, piecewise-linear, concave utilitiesMarket equilibrium under separable, piecewise-linear, concave utilities

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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