IDEAS home Printed from
   My bibliography  Save this paper

Game complete analysis of Bertrand Duopoly


  • Carfì, David
  • Perrone, Emanuele


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

    Download full text from publisher

    File URL:
    File Function: original version
    Download Restriction: no

    References listed on IDEAS

    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 Economic Fields, ASERS Publishing, vol. 0(1), pages 23-36, June.
    3. David C. Wyld, 2010. "ASecond Life for organizations?: managing in the new, virtual world," Management Research Review, Emerald Group Publishing, vol. 33(6), pages 529-562, May.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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. 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.
    3. Carfì, David & Fici, Caterina, 2012. "The government-taxpayer game," MPRA Paper 38506, University Library of Munich, Germany.

    More about this item


    Duopoly; Normal form Games; Microeconomic Policy; Complete study; Bargaining solutions;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:31302. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.