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Computing the Arrow-Debreu Competitive Market Equilibrium and Its Extensions

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Algorithmic Applications in Management (AAIM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3521))

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Abstract

We consider the Arrow-Debreu competitive market equilibrium problem which was first formulated by Leon Walras in 1874 [12]. In this problem every one in a population of n players has an initial endowment of a divisible good and a utility function for consuming all goods—own and others. Every player sells the entire initial endowment and then uses the revenue to buy a bundle of goods such that his or her utility function is maximized. Walras asked whether prices could be set for everyone’s good such that this is possible. An answer was given by Arrow and Debreu in 1954 [1] who showed that such equilibrium would exist if the utility functions were concave. Their proof was non-constructive and did not offer any algorithm to find such equilibrium prices.

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Authors and Affiliations

  1. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA

    Yinyu Ye

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  1. Yinyu Ye
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Editors and Affiliations

  1. IBM Almaden Research Center, 650 Harry Road, 95120, San Jose, CA,  

    Nimrod Megiddo

  2. The State Key Lab for Manufacturing Systems Engineering, 710049, Xi’an, P.R. China

    Yinfeng Xu

  3. Department of Computer Science, Montana State University, 59717, Bozeman, MT, USA

    Binhai Zhu

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Ye, Y. (2005). Computing the Arrow-Debreu Competitive Market Equilibrium and Its Extensions. In: Megiddo, N., Xu, Y., Zhu, B. (eds) Algorithmic Applications in Management. AAIM 2005. Lecture Notes in Computer Science, vol 3521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496199_2

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  • DOI: https://doi.org/10.1007/11496199_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26224-4

  • Online ISBN: 978-3-540-32440-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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