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Cournot's model of competition is typically presented for the case of a duopoly market structure; the following example provides a straightforward analysis of the Cournot model for the case of Duopoly. Therefore, suppose we have a market consisting of only two firms which we will call firm 1 and firm 2.
The Bertrand model has similar assumptions to the Cournot model: Two firms; Homogeneous products; Both firms know the market demand curve; However, unlike the Cournot model, it assumes that firms have the same MC. It also assumes that the MC is constant. The Bertrand model, in which, in a game of two firms, competes in price instead of output ...
The Cournot duopoly model developed in his book also introduced the concept of a (pure strategy) Nash equilibrium, the reaction function and best-response dynamics. Cournot believed that economists must utilize the tools of mathematics only to establish probable limits and to express less stable facts in more absolute terms.
The first use of the Nash equilibrium was in the Cournot duopoly as developed by Antoine Augustin Cournot in his 1838 book. [4] Both firms produce a homogenous product: given the total amount supplied by the two firms, the (single) industry price is determined using the demand curve.
Duopoly, a case of an oligopoly where two firms operate and have power over the market. [8] Example: Aircraft manufactures: Boeing and Airbus. A duopoly in theory could have the same effect as a monopoly on pricing within a market if they were to collude on prices and or output of goods.
Competition is well defined through the Cournot's model because, when there are infinite many firms in the market, the excess of price over marginal cost will approach to zero. [4] A duopoly is a special form of oligopoly where the market is made up of only two firms.
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In 1838, Antoine Augustin Cournot provided a model of competition in oligopolies. Though he did not refer to it as such, he presented a solution that is the Nash equilibrium of the game in his Recherches sur les principes mathématiques de la théorie des richesses ( Researches into the Mathematical Principles of the Theory of Wealth ).