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Oligopoly model with interdependent preferences: existence and uniqueness of Nash equilibrium

Author

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  • Marco F. Boretto
  • Fausto Cavalli
  • Ahmad Naimzada

Abstract

We propose a model to describe and study the effect of social interdependent preferences in a Cournot oligopoly based on a game in which the utility functions of firms depend on a combination of weighted profits of their competitors. If social interaction is neglected, the model reduces to the classic Cournot game, diverting from it as the role of social interaction becomes more and more relevant. Several synthetic measures are proposed to summarize the overall behavior of the agents and some configurations characterized by particular interactional structures are presented. Finally, the study of the well-posedness of the proposed framework is investigated, in terms of the existence and uniqueness of Nash equilibria. To this end, we generalize the conditions under which the existence and/or uniqueness of Nash equilibrium in classic game is guaranteed for particular Cournotian oligopoly models without interdependent preferences. In particular, we focus on two families of oligopolies, respectively consisting of "concave" oligopolies and oligopolies with isoelastic demand function.

Suggested Citation

  • Marco F. Boretto & Fausto Cavalli & Ahmad Naimzada, 2021. "Oligopoly model with interdependent preferences: existence and uniqueness of Nash equilibrium," Working Papers 462, University of Milano-Bicocca, Department of Economics, revised Mar 2021.
    • Handle: RePEc:mib:wpaper:462
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    1. Marco F. Boretto & Fausto Cavalli & Ahmad Naimzada, 2021. "Comparative statics and centrality measures in oligopolies with interdependent preferences," Working Papers 464, University of Milano-Bicocca, Department of Economics, revised Mar 2021.
    2. Marco F. Boretto & Fausto Cavalli & Ahmad Naimzada, 2021. "Characterization of Nash equilibria in Cournotian oligopolies with interdependent preferences," Working Papers 463, University of Milano-Bicocca, Department of Economics, revised Mar 2021.

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    More about this item

    Keywords

    Cournot Game; Preference interdependence; Network; Nash Equilibrium; existence and uniqueness;
    All these keywords.

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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