Game complete analysis of Bertrand Duopoly

David Carfì () and Emanuele Perrone

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Duopoly; Normal form Games; Microeconomic Policy; Complete study; Bargaining solutions (search for similar items in EconPapers)
JEL-codes: C7 C71 C72 C81 D0 D01 (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-com and nep-ind
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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