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A rational convex program for linear Arrow-Debreu markets

Author

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  • Devanur, Nikhil R.
  • Garg, Jugal
  • Végh, László A.

Abstract

We present a new flow-type convex program describing equilibrium solutions to linear Arrow-Debreu markets. Whereas convex formulations were previously known ([Nenakov and Primak 1983; Jain 2007; Cornet 1989]), our program exhibits several new features. It provides a simple necessary and sufficient condition and a concise proof of the existence and rationality of equilibria, settling an open question raised by Vazirani [2012]. As a consequence, we also obtain a simple new proof of the result in Mertens [2003] that the equilibrium prices form a convex polyhedral set.

Suggested Citation

  • Devanur, Nikhil R. & Garg, Jugal & Végh, László A., 2016. "A rational convex program for linear Arrow-Debreu markets," LSE Research Online Documents on Economics 69224, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:69224
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    File URL: https://researchonline.lse.ac.uk/id/eprint/69224/
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    References listed on IDEAS

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    1. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, January.
    2. William C. Brainard & Herbert E. Scarf, 2005. "How to Compute Equilibrium Prices in 1891," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 57-83, January.
    3. Gale, David, 1976. "The linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 205-209, July.
    4. Nisan,Noam & Roughgarden,Tim & Tardos,Eva & Vazirani,Vijay V. (ed.), 2007. "Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9780521872829, January.
    5. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    6. Eaves, B. Curtis, 1976. "A finite algorithm for the linear exchange model," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 197-203, July.
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    Cited by:

    1. Vijay V. Vazirani, 2025. "Arctic Auctions, Linear Fisher Markets, and Rational Convex Programs," Papers 2511.21637, arXiv.org.
    2. Jugal Garg & Thorben Trobst & Vijay V. Vazirani, 2020. "One-Sided Matching Markets with Endowments: Equilibria and Algorithms," Papers 2009.10320, arXiv.org, revised Jul 2021.
    3. Marianna Eisenberg-Nagy & Tibor Illés & Gábor Lovics, 2019. "Market exchange models and geometric programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 415-435, June.
    4. Simina Br^anzei & Nikhil R. Devanur & Yuval Rabani, 2019. "Proportional Dynamics in Exchange Economies," Papers 1907.05037, arXiv.org, revised Sep 2023.

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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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