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Stochastic stability in the Scarf economy

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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 12066r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jun 2013.
    • Handle: RePEc:mse:cesdoc:12066r
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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. 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.
    4. 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.
    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. 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.
    7. repec:hal:pseose:halshs-01296646 is not listed on IDEAS
    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

    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

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