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Noncooperative oligopoly equilibrium in markets with hierarchical competition

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  • Ludovic A. Julien

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper deals with the existence of a non-cooperative sequential equilibrium in interrelated markets with heterogeneous atomic traders. Since this model features a rich set of strategic interactions, there are two kinds of problems associated with the existence of equilibrium. First, existence and uniqueness of followers' strategies are not guaranteed. Second, the no-trade equilibrium is always an equilibrium outcome. To overcome these two difficulties we consider a differentiable approach. We show that the set of equations which determines the strategies of followers is a variety with the required dimension, i.e. the vector mapping which defines this set is a local C²-diffeomorphism. The continuous differentiability of followers' strategies is critical for the existence of an interior equilibrium. Unlike the simultaneous move games, exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade. Some examples buttress the approach and discuss the assumptions made on the primitives.

Suggested Citation

  • Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," Working Papers hal-04159741, HAL.
    • Handle: RePEc:hal:wpaper:hal-04159741
    Note: View the original document on HAL open archive server: https://hal.science/hal-04159741
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    References listed on IDEAS

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    More about this item

    Keywords

    Pure strategies; diffeomorphisms; Stackelberg-Nash equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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