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Spending Is Not Easier Than Trading: On the Computational Equivalence of Fisher and Arrow-Debreu Equilibria

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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Abstract

It is a common belief that computing a market equilibrium in Fisher’s spending model is easier than computing a market equilibrium in Arrow-Debreu’s exchange model. This belief is built on the fact that we have more algorithmic success in Fisher equilibria than Arrow-Debreu equilibria. For example, a Fisher equilibrium in a Leontief market can be found in polynomial time, while it is PPAD-hard to compute an approximate Arrow-Debreu equilibrium in a Leontief market.

In this paper, we show that even when all the utilities are additively separable, piecewise-linear and concave, computing an approximate equilibrium in Fisher’s model is PPAD-hard. Our result solves a long-term open question on the complexity of market equilibria. To the best of our knowledge, this is the first PPAD-hardness result for Fisher’s model.

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Author information

Authors and Affiliations

  1. Princeton University,  

    Xi Chen

  2. University of Southern California,  

    Shang-Hua Teng

Authors
  1. Xi Chen
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  2. Shang-Hua Teng
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Chen, X., Teng, SH. (2009). Spending Is Not Easier Than Trading: On the Computational Equivalence of Fisher and Arrow-Debreu Equilibria. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_66

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_66

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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