IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/12066.html
   My bibliography  Save this paper

Stochastic stability in the Scarf economy

Author

Listed:

Abstract

We present a mathematical model for the analysis of the bargaining games based on private prices used by Gintis to simulate the dynamics of prices in exchange economies, see [Gintis 2007]. We then characterize, in the Scarf economy, a class of dynamics for which the Walrasian equilibrium is the only stochastically stable state. Hence, we provide dynamic foundations for general equilibrium for one of the best-known example of instability of the tâtonement process

Suggested Citation

  • Antoine Mandel & Herbert Gintis, 2012. "Stochastic stability in the Scarf economy," Documents de travail du Centre d'Economie de la Sorbonne 12066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:12066
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    2. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    3. 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.
    4. Bottazzi, Jean-Marc, 1994. "Accessibility of Pareto optima by Walrasian exchange processes," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 585-603, November.
    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. 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.
    8. Herbert E. Scarf, 1969. "An Example of an Algorithm for Calculating General Equilibrium," Cowles Foundation Discussion Papers 276, Cowles Foundation for Research in Economics, Yale University.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    11. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
    12. Roberto Serrano & Oscar Volij, 2003. "MISTAKE IN COOPERATION:the Stochastic Stability of Edgeworth's Recontracting," Working Papers 2003-23, Brown University, Department of Economics.
    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. Sonnenschein, Hugo, 1973. "Do Walras' identity and continuity characterize the class of community excess demand functions?," Journal of Economic Theory, Elsevier, vol. 6(4), pages 345-354, August.
    15. Scarf, Herbert, 1969. "An Example of an Algorithm for Calculating General Equilibrium Prices," American Economic Review, American Economic Association, vol. 59(4), pages 669-677, Part I Se.
    16. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    17. Herbert Gintis, 2007. "The Dynamics of General Equilibrium," Economic Journal, Royal Economic Society, vol. 117(523), pages 1280-1309, October.
    18. Schecter, Stephen, 1977. "Accessibility of optima in pure exchange economies," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 197-216, December.
    19. Sean Crockett, 2013. "Price Dynamics In General Equilibrium Experiments," Journal of Economic Surveys, Wiley Blackwell, vol. 27(3), pages 421-438, July.
    20. Arkit, Aleksandra, 2003. "Globally stable price dynamics," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 27-38, February.
    21. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    22. Scarf, Herbert, 1981. "Comment on: "On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example"," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 469-470, June.
    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. Gerard Ballot & Antoine Mandel & Annick Vignes, 2015. "Agent-based modeling and economic theory: where do we stand?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 199-220, October.
    2. Mandel, Antoine & Gintis, Herbert, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 84-92.
    3. 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.
    4. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2017. "Trader matching and the selection of market institutions," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 118-127.
    5. Суслов В.И. & Доможиров Д.А. & Ибрагимов Н.М. & Костин В.С. & Мельникова Л.В. & Цыплаков А.А., 2016. "Агент-Ориентированная Многорегиональная Модель “Затраты-Выпуск” Российской Экономики," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 52(1), pages 112-131, январь.
    6. Rabani, Yuval & Schulman, Leonard J., 2021. "The invisible hand of Laplace: The role of market structure in price convergence and oscillation," Journal of Mathematical Economics, Elsevier, vol. 95(C).

    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. Mandel, Antoine & Gintis, Herbert, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 84-92.
    2. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    3. Gaël Giraud, 2004. "The limit-price exchange process," Cahiers de la Maison des Sciences Economiques b04118, Université Panthéon-Sorbonne (Paris 1).
    4. Daniele Cassese & Paolo Pin, 2018. "Decentralized Pure Exchange Processes on Networks," Papers 1803.08836, arXiv.org, revised Mar 2022.
    5. Roland Pongou & Roberto Serrano, 2009. "A Dynamic Theory of Fidelity Networks with an Application to the Spread of HIV/AIDS," Working Papers 2009-2, Brown University, Department of Economics.
    6. Gerard Ballot & Antoine Mandel & Annick Vignes, 2015. "Agent-based modeling and economic theory: where do we stand?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 199-220, October.
    7. 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.
    8. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.
    9. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    10. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    11. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. Newton, Jonathan, 2015. "Stochastic stability on general state spaces," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 46-60.
    13. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    14. Aad Ruiter, 2020. "Approximating Walrasian Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 577-596, February.
    15. Bilancini, Ennio & Boncinelli, Leonardo & Newton, Jonathan, 2020. "Evolution and Rawlsian social choice in matching," Games and Economic Behavior, Elsevier, vol. 123(C), pages 68-80.
    16. Dai, Darong, 2012. "On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness," MPRA Paper 40560, University Library of Munich, Germany.
    17. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    18. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    19. 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.
    20. Kandori, Michihiro & Serrano, Roberto & Volij, Oscar, 2008. "Decentralized trade, random utility and the evolution of social welfare," Journal of Economic Theory, Elsevier, vol. 140(1), pages 328-338, May.

    More about this item

    Keywords

    General Equilibrium; exchange economies; bargaining games; stochastic stability;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mse:cesdoc:12066. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.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.