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Globally and Universally Convergent Price Adjustment Processes

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  • Herings, P.J.J.

    (Tilburg University, School of Economics and Management)

Abstract

We discuss three processes of price adjustment in an exchange economy, proposed by Smale (1976), van der Laan and Talman (1987), and Kamiya (1990), respectively. Under a regularity condition on the economy, the first process is guaranteed to converge to a competitive equilibrium for almost every initial price system such that one of the prices is equal to zero. The process of Kamiya (1990) is guaranteed to converge to the set of competitive equilibria for almost every initial price system, under a condition on the boundary behavior of the excess demand function of the economy. The (van der Laan and Talman 1987) process was shown by Herings (1997) to converge to a competitive equilibrium for a generic set of exchange economies for any initial price system. The simplest way to describe these processes is by characterizing the path of prices that they generate. Convergence proofs then rely on results from differential topology and establish that these paths have a manifold structure. The required tools, involving regular constraint sets and manifolds with generalized boundary, are explained in detail and can be fruitfully applied in other domains as well. The paper concludes with an overview of globally and universally convergent processes in other environments like production economies, economies with price rigidities, and game theory.
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Suggested Citation

  • Herings, P.J.J., 2024. "Globally and Universally Convergent Price Adjustment Processes," Other publications TiSEM 12dc4fc2-19e8-4a8c-b2ff-2, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:12dc4fc2-19e8-4a8c-b2ff-2a9346f0647a
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    References listed on IDEAS

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    1. Philippe Bich & Lisa Morhaim, 2020. "On the existence of Pairwise stable weighted networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03969712, HAL.
    2. van den Elzen, Antoon & Kremers, Hans, 2006. "An adjustment process for nonconvex production economies," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 1-13, February.
    3. Philippe Bich & Lisa Morhaim, 2020. "On the existence of Pairwise stable weighted networks," PSE-Ecole d'économie de Paris (Postprint) halshs-03969712, HAL.
    4. 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.
    5. Philippe Bich & Lisa Morhaim, 2020. "On the existence of Pairwise stable weighted networks," Post-Print halshs-03969712, HAL.
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    12. P. Jean-Jacques Herings & Ronald J.A.P. Peeters, 2001. "symposium articles: A differentiable homotopy to compute Nash equilibria of n -person games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 159-185.
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