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

  • Xi Chen
  • Shang-Hua Teng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

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.

Keywords

Utility Function Nash Equilibrium Market Equilibrium Price Vector Annual IEEE Symposium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Xi Chen
    • 1
  • Shang-Hua Teng
    • 2
  1. 1.Princeton University 
  2. 2.University of Southern California 

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