IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/69224.html
   My bibliography  Save this paper

A rational convex program for linear Arrow-Debreu markets

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/69224/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Simina Br^anzei & Nikhil R. Devanur & Yuval Rabani, 2019. "Proportional Dynamics in Exchange Economies," Papers 1907.05037, arXiv.org, revised Sep 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simina Br^anzei & Nikhil R. Devanur & Yuval Rabani, 2019. "Proportional Dynamics in Exchange Economies," Papers 1907.05037, arXiv.org, revised Sep 2023.
    2. M. Florig, 2004. "Equilibrium Correspondence of Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 97-109, January.
    3. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Continuity and Uniqueness of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 237-263, May.
    4. Jean-Marc Bonnisseau & Michael Florig, 2003. "Existence and optimality of oligopoly equilibria in linear exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 727-741, November.
    5. Simina Br^anzei & Fedor Sandomirskiy, 2019. "Algorithms for Competitive Division of Chores," Papers 1907.01766, arXiv.org, revised Jul 2023.
    6. Konovalov, Alexander & Marakulin, Valeri, 2006. "Equilibria without the survival assumption," Journal of Mathematical Economics, Elsevier, vol. 42(2), pages 198-215, April.
    7. Konovalov, A. & Marakulin, V., 2001. "Equilibria Without the Survival Assumption : A Non-Standard Analysis Approach," Discussion Paper 2001-34, Tilburg University, Center for Economic Research.
    8. Florig, Michael & Rivera, Jorge, 2019. "Walrasian equilibrium as limit of competitive equilibria without divisible goods," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 1-8.
    9. Monique Florenzano & Emma Moreno-García, 2001. "Linear exchange economies with a continuum of agents," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(4), pages 253-272.
    10. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    11. Bottazzi, Jean-Marc & De Meyer, Bernard, 2003. "A market game for assets and taxed investors," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 657-675, July.
    12. Konovalov, A. & Marakulin, V., 2002. "Generalized equilibrium in an economy without the survival assumption," Econometric Institute Research Papers EI 2002-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Florig, Michael, 2001. "Hierarchic competitive equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(4), pages 515-546, July.
    14. J. M. Bonnisseau & M. Florig & A. Jofré, 2001. "Differentiability of Equilibria for Linear Exchange Economies," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 265-288, May.
    15. Rahul Garg & Sanjiv Kapoor, 2006. "Auction Algorithms for Market Equilibrium," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 714-729, November.
    16. Dubey, Pradeep & Sondermann, Dieter, 2009. "Perfect competition in an oligopoly (including bilateral monopoly)," Games and Economic Behavior, Elsevier, vol. 65(1), pages 124-141, January.
    17. Sprumont, Yves, 2013. "Constrained-optimal strategy-proof assignment: Beyond the Groves mechanisms," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1102-1121.
    18. Gaël Giraud & Céline Rochon, 2010. "Transition to Equilibrium in International Trades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00657038, HAL.
    19. Michael Florig & Jorge Rivera Cayupi, 2015. "Walrasian equilibrium as limit of a competitive equilibrium without divisible goods," Working Papers wp404, University of Chile, Department of Economics.
    20. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.

    More about this item

    Keywords

    market equilibrium; linear exchange market; convex programming;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:69224. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.