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Game complete analysis of Bertrand 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] and [9]) and al-ready employed by himself and others in [4], [5], [7]) to the classic Bertrand Duopoly (1883), 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 unit prices of their product, contrary to the Cournot duopoly, in which the enterprises decide to use the quantities of the commodity produced as strategies. The main solutions proposed in literature for this kind of duopoly (as in the case of Cournot 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 Bertrand Duopoly as a differentiable game (games 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 Bertrand 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 pricing-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, 2011. "Game complete analysis of Bertrand Duopoly," MPRA Paper 31302, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:31302
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    References listed on IDEAS

    as
    1. Carfì, David, 2009. "Differentiable game complete analysis for tourism firm decisions," MPRA Paper 29193, University Library of Munich, Germany.
    2. David CARFÌ & Daniele SCHILIRÒ, 2011. "Crisis In The Euro Area: Coopetitive Game Solutions As New Policy Tools," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 2(1), pages 22-36.
    3. David C. Wyld, 2010. "ASecond Lifefor organizations?: managing in the new, virtual world," Management Research Review, Emerald Group Publishing Limited, vol. 33(6), pages 529-562, May.
    4. repec:srs:journl:tpref:v:2:y:2011:i:1:p:22-36 is not listed on IDEAS
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    Cited by:

    1. David, Carfì & Daniele, SCHILIRO', 2014. "Improving competitiveness and trade balance of Greek economy: a coopetitive strategy model," MPRA Paper 76970, University Library of Munich, Germany.
    2. Carfì, David & Schilirò, Daniele, 2011. "A framework of coopetitive games: applications to the Greek crisis," MPRA Paper 78089, University Library of Munich, Germany.
    3. Carfì, David & Donato, Alessia & Schilirò, Daniele, 2018. "An environmentally sustainable global economy. A coopetitive model," MPRA Paper 86718, University Library of Munich, Germany.
    4. Tiru Arthanari & David Carfì & Francesco Musolino, 2015. "Game Theoretic Modeling of Horizontal Supply Chain Coopetition among Growers," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-22.
    5. Carfí, David & Musolino, Francesco, 2014. "Speculative and hedging interaction model in oil and U.S. dollar markets with financial transaction taxes," Economic Modelling, Elsevier, vol. 37(C), pages 306-319.

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    Keywords

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    JEL classification:

    • D0 - Microeconomics - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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