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Natural Instability of Equilibrium Prices

Author

Listed:
  • Dmitry Levando

    () (National Research University Higher School of Economics, Moscow, Russia)

  • Maxim Sakharov

    (Bauman Mstu, Moscow, Russia)

Abstract

We develop a theory of market fluctuations caused by strategic trade with complete information and without outside shocks. The constructed general equilibrium duopoly is a strategic market game with infinite strategies and multiple mixed strategies equilibria. First order conditions (FOC) of the game are the ill-posed problems (Hadamard, 1909), but every equilibrium mixed strategy can be only approximated. This imposes restrictions on convergence of common beliefs of players about actions of each other, existence of rational expectations and a price discovery property of the market, although the market is informationally efficient (Fama, 1970). We suggest a modification of Tikhonov regularization to construct pseudo-solutions. All endogenous variables of the model are exposed to unremovable instabilities, ‘natural instabilities’, specific to parameters of a chosen approximation. Our result is also related to existence of common knowledge, sun-spot equilibrium, and noise trade.

Suggested Citation

  • Dmitry Levando & Maxim Sakharov, 2018. "Natural Instability of Equilibrium Prices," Working Papers 2018:01, Department of Economics, University of Venice "Ca' Foscari".
  • Handle: RePEc:ven:wpaper:2018:01
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Strategic market games; ill-posed problems; common knowledge; rational expectations; efficient market; price fluctuations;

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D59 - Microeconomics - - General Equilibrium and Disequilibrium - - - Other
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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