IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-01296646.html
   My bibliography  Save this paper

Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium

Author

Listed:
  • Antoine Mandel

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Herbert Gintis

    (Santa Fe Institute)

Abstract

We introduce, in the standard exchange economy model, market games in which agents use private prices as strategies. We give conditions on the game form that ensure that the only strict Nash equilibria of the game are the competitive equilibria of the underlying economy. This equivalence result has two main corollaries. First, it adds to the evidence that competitive equilibria can be strategically stable even in small economies. Second, it implies that competitive equilibria have good local stability properties under a large class of evolutionary learning dynamics.

Suggested Citation

  • Antoine Mandel & Herbert Gintis, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Post-Print halshs-01296646, HAL.
    • Handle: RePEc:hal:journl:halshs-01296646
    DOI: 10.1016/j.jmateco.2015.12.008
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01296646
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01296646/document
    Download Restriction: no
    File URL: https://libkey.io/10.1016/j.jmateco.2015.12.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Mandel, Antoine & Gintis, Herbert, 2014. "Stochastic stability in the Scarf economy," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 44-49.
    3. Chongmin Kim & Kam-Chau Wong, 2011. "Evolution of Walrasian equilibrium in an exchange economy," Journal of Evolutionary Economics, Springer, vol. 21(4), pages 619-647, October.
    4. Jacques Lesourne & André Orléan & Bernard Walliser, 2006. "Evolutionary Microeconomics," Springer Books, Springer, number 978-3-540-28537-3, June.
    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
    7. Smith, Vernon L, 1982. "Microeconomic Systems as an Experimental Science," American Economic Review, American Economic Association, vol. 72(5), pages 923-955, December.
    8. Anderson, Christopher M. & Plott, Charles R. & Shimomura, K.-I.Ken-Ichi & Granat, Sander, 2004. "Global instability in experimental general equilibrium: the Scarf example," Journal of Economic Theory, Elsevier, vol. 115(2), pages 209-249, April.
    9. Alos-Ferrer, Carlos & Ania, Ana B. & Schenk-Hoppe, Klaus Reiner, 2000. "An Evolutionary Model of Bertrand Oligopoly," Games and Economic Behavior, Elsevier, vol. 33(1), pages 1-19, October.
    10. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    11. Gjerstad, Steven & Dickhaut, John, 1998. "Price Formation in Double Auctions," Games and Economic Behavior, Elsevier, vol. 22(1), pages 1-29, January.
    12. Ghosal, Sayantan & Morelli, Massimo, 2004. "Retrading in market games," Journal of Economic Theory, Elsevier, vol. 115(1), pages 151-181, March.
    13. Alok Kumar & Martin Shubik, 2004. "Variations on the Theme of Scarf's Counter-Example," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 1-19, August.
    14. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    15. Mandel, Antoine & Landini, Simone & Gallegati, Mauro & Gintis, Herbert, 2015. "Price dynamics, financial fragility and aggregate volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 257-277.
    16. Pierre Dockès & Jean-Pierre Potier, 2005. "Léon Walras et le statut de la concurrence : une étude à partir des Elements d'économie politique pure," Post-Print halshs-00138352, HAL.
    17. Friedman, Daniel, 1991. "A simple testable model of double auction markets," Journal of Economic Behavior & Organization, Elsevier, vol. 15(1), pages 47-70, January.
    18. Herbert Gintis, 2007. "The Dynamics of General Equilibrium," Economic Journal, Royal Economic Society, vol. 117(523), pages 1280-1309, October.
    19. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    20. repec:hal:pseose:halshs-01152302 is not listed on IDEAS
    21. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
    22. Ianni, Antonella, 2014. "Learning strict Nash equilibria through reinforcement," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 148-155.
    23. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    24. Mandel Antoine & Botta Nicola, 2009. "A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-18, December.
    25. Duffy, John & Matros, Alexander & Temzelides, Ted, 2011. "Competitive behavior in market games: Evidence and theory," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1437-1463, July.
    26. Kunimoto, Takashi & Serrano, Roberto, 2004. "Bargaining and competition revisited," Journal of Economic Theory, Elsevier, vol. 115(1), pages 78-88, March.
    27. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
    28. Peck, James & Shell, Karl, 1990. "Liquid markets and competition," Games and Economic Behavior, Elsevier, vol. 2(4), pages 362-377, December.
    29. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    30. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    31. Yves Balasko, 2009. "The Equilibrium Manifold: Postmodern Developments in the Theory of General Economic Equilibrium," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262026546, April.
    32. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
    33. Gale, Douglas M, 1986. "Bargaining and Competition Part II: Existence," Econometrica, Econometric Society, vol. 54(4), pages 807-818, July.
    34. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    35. repec:hal:pseose:halshs-00977572 is not listed on IDEAS
    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. Tongkui Yu & Shu-Heng Chen, 2021. "Realizable Utility Maximization as a Mechanism for the Stability of Competitive General Equilibrium in a Scarf Economy," Computational Economics, Springer;Society for Computational Economics, vol. 58(1), pages 133-167, June.
    2. Marian Leimbach & Anselm Schultes & Lavinia Baumstark & Anastasis Giannousakis & Gunnar Luderer, 2017. "Solution algorithms for regional interactions in large-scale integrated assessment models of climate change," Annals of Operations Research, Springer, vol. 255(1), pages 29-45, August.
    3. Hudik, Marek, 2021. "Push factors of endogenous institutional change," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 504-514.

    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. repec:hal:pseose:halshs-01296646 is not listed on IDEAS
    2. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    3. Mandel, Antoine & Gintis, Herbert, 2014. "Stochastic stability in the Scarf economy," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 44-49.
    4. Penta, Antonio, 2011. "Multilateral bargaining and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 417-424.
    5. Herbert Gintis & Antoine Mandel, 2012. "The Stability of Walrasian General Equilibrium," Documents de travail du Centre d'Economie de la Sorbonne 12065r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2013.
    6. Maria-Augusta Miceli & Federico Cecconi & Giovanni Cerulli, 2013. "Walrasian Tatonnement by Sequential Pairwise Trading: Convergence and Welfare Implications," Working Papers in Public Economics 161, University of Rome La Sapienza, Department of Economics and Law.
    7. Duffy, John & Matros, Alexander & Temzelides, Ted, 2011. "Competitive behavior in market games: Evidence and theory," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1437-1463, July.
    8. Ghosal, Sayantan & Porter, James, 2010. "Out-Of-Equilibrium Dynamics With Decentralized Exchange: Cautious Trading And Convergence To Efficiency," Economic Research Papers 271179, University of Warwick - Department of Economics.
    9. Penta, Antonio, 2007. "Collective Bargaining and Walrasian Equilibrium," MPRA Paper 10260, University Library of Munich, Germany, revised Sep 2007.
    10. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    11. Gale, Douglas & Sabourian, Hamid, 2006. "Markov equilibria in dynamic matching and bargaining games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 336-352, February.
    12. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    13. Kazuya Kamiya & Takashi Shimizu, 2006. "A Dynamic General Equilibrium Model with Centralized Auction Markets," CIRJE F-Series CIRJE-F-417, CIRJE, Faculty of Economics, University of Tokyo.
    14. Sjur Didrik Flåm, 2020. "Emergence of price-taking Behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 847-870, October.
    15. John Duffy & Alexander Matros & Ted Temzelides, 2008. "Competitive Behavior in Market Games: Evidence and Theory," Working Paper 366, Department of Economics, University of Pittsburgh, revised Jul 2010.
    16. Zigrand, Jean-Pierre, 2006. "Endogenous market integration, manipulation and limits to arbitrage," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 301-314, June.
    17. Spulber, Daniel F., 2016. "Patent licensing and bargaining with innovative complements and substitutes," Research in Economics, Elsevier, vol. 70(4), pages 693-713.
    18. Ghosal, Sayantan & Morelli, Massimo, 2004. "Retrading in market games," Journal of Economic Theory, Elsevier, vol. 115(1), pages 151-181, March.
    19. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    20. Dmitry Levando, 2012. "A Survey Of Strategic Market Games," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 57(194), pages 63-106, July - Se.
    21. Ghosal, Sayantan & Porter, James, 2013. "Decentralised exchange, out-of-equilibrium dynamics and convergence to efficiency," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 1-21.

    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:hal:journl:halshs-01296646. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.