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Stochastic Stability in the Scarf Economy

Author

Listed:
  • Antoine Mandel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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)

  • Herbert Gintis

    (CEU - Central European University [Budapest, Hongrie], Santa Fe Institute)

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 in 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, 2014. "Stochastic Stability in the Scarf Economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00977572, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00977572
    DOI: 10.1016/j.mathsocsci.2013.09.002
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    References listed on IDEAS

    as
    1. 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.
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    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.
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    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. repec:hal:pseose:halshs-01296646 is not listed on IDEAS
    5. 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.
    6. Arjun Jayadev & Suresh Naidu, 2024. "“Be Serious!†: In Memoriam Herb Gintis," Review of Radical Political Economics, Union for Radical Political Economics, vol. 56(1), pages 140-145, March.
    7. 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.
    8. 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).

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    More about this item

    Keywords

    Stochastic Stability; General Equilibrium;

    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

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