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Game complete analysis of Bertrand Duopoly

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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31302.

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Date of creation: 2011
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Handle: RePEc:pra:mprapa:31302

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

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References

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  1. Carfì, David, 2009. "Reactivity in decision-form games," MPRA Paper 29001, University Library of Munich, Germany.
  2. Carfì, David & Schilirò, Daniele, 2010. "Crisis in the Euro area: coopetitive game solutions as new policy tools," MPRA Paper 31891, University Library of Munich, Germany, revised 26 Jun 2011.
  3. Carfì, David & Ricciardello, Angela, 2009. "Non-reactive strategies in decision-form games," MPRA Paper 29262, University Library of Munich, Germany.
  4. Carfì, David & Ricciardello, Angela, 2011. "Mixed extensions of decision-form games," MPRA Paper 28971, University Library of Munich, Germany.
  5. Carfì, David, 2009. "Differentiable game complete analysis for tourism firm decisions," MPRA Paper 29193, University Library of Munich, Germany.
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Cited by:
  1. Carfì, David & Fici, Caterina, 2012. "The government-taxpayer game," MPRA Paper 38506, 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. David, Carfì & Daniele, SCHILIRO', 2014. "Improving competitiveness and trade balance of Greek economy: a coopetitive strategy model," MPRA Paper 55124, University Library of Munich, Germany.

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