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Game complete analysis of symmetric Cournot duopoly

Author

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  • Carfì, David
  • Perrone, Emanuele

Abstract

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8], [9], and already employed by himself and others in [4], [5], [7]) to the classic Cournot Duopoly (1838), classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ, as possible strategies, the quantities of the commodity produced. The main solutions proposed in literature for this kind of duopoly are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Cournot Duopoly as a differentiable game (a game with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Cournot game (this also in asymmetric cases with the help of computers) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise decisions are considered, and we show how the complete study gives a real extremely extended comprehension of the classic model.

Suggested Citation

  • Carfì, David & Perrone, Emanuele, 2012. "Game complete analysis of symmetric Cournot duopoly," MPRA Paper 35930, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:35930
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    File URL: https://mpra.ub.uni-muenchen.de/35930/1/MPRA_paper_35930.pdf
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    Cited by:

    1. Carfì, David & Schilirò, Daniele, 2012. "A model of coopetitive game for the environmental sustainability of a global green economy," MPRA Paper 38508, University Library of Munich, Germany.
    2. Carfì, David & Schilirò, Daniele, 2012. "Global green economy and environmental sustainability: a coopetitive model," MPRA Paper 37018, University Library of Munich, Germany.
    3. Carfì, David & Bagileri, Daniela & Dagnino, Gianbattista, 2012. "Asymmetric R&D alliances and coopetitive games," MPRA Paper 37095, University Library of Munich, Germany.
    4. repec:wsi:igtrxx:v:17:y:2015:i:02:n:s0219198915400137 is not listed on IDEAS
    5. Carfì, David & Fici, Caterina, 2012. "The government-taxpayer game," MPRA Paper 38506, University Library of Munich, Germany.
    6. Daniela Baglieri & David Carf`i & Giovanni Battista Dagnino, 2012. "Asymmetric R&D Alliances and Coopetitive Games," Papers 1205.2878, arXiv.org.

    More about this item

    Keywords

    duopoly; normal-form games; microeconomic Policy; complete study of differentiable games; bargaining solutions;

    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • O12 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Microeconomic Analyses of Economic Development
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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