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Quasivariational inequalities for dynamic competitive economic equilibrium problems in discrete time

Author

Listed:
  • Shapour Heidarkhani

    (Razi University)

  • David Barilla

    (Messina University)

  • Giuseppe Caristi

    (Messina University)

Abstract

Equilibrium is a central concept in numerous disciplines including economics, management science, operations research, and engineering. We are concerned with an evolutionary quasivariational inequality which is connected to discrete dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. We study the discrete equilibrium problem by means of a discrete time-dependent quasivariational inequality in the discrete space $$\ell ^2([0,T]_{\mathbb {Z}},\mathbb {R})$$ ℓ 2 ( [ 0 , T ] Z , R ) . We ensure an existence result of discrete time-dependent equilibrium solutions. Finally, we show the stability of equilibrium in a completely decentralized Walrasian general equilibrium economy in which prices are fully controlled by economic agents, with production and trade occurring out of equilibrium.

Suggested Citation

  • Shapour Heidarkhani & David Barilla & Giuseppe Caristi, 2023. "Quasivariational inequalities for dynamic competitive economic equilibrium problems in discrete time," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 277-304, June.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:1:d:10.1007_s10203-022-00385-8
    DOI: 10.1007/s10203-022-00385-8
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    References listed on IDEAS

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    1. Laura Scrimali, 2008. "The financial equilibrium problem with implicit budget constraints," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 191-203, June.
    2. 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.
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    More about this item

    Keywords

    Competitive economic equilibrium; Discrete dynamic; Walras law; Utility function; Discrete space; Variational inequality;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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