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Cournot presents a mathematically correct analysis of the equilibrium condition corresponding to a certain logically consistent model of duopolist behaviour. However his model is not stated and is not particularly natural ( Shapiro remarked that observed practice constituted a "natural objection to the Cournot quantity model" [ 9 ] ), and "his ...
A Cournot equilibrium occurs when each firm's output maximizes its profits given the output of the other firms, which is a pure-strategy Nash equilibrium. Cournot also introduced the concept of best response dynamics in his analysis of the stability of equilibrium. Cournot did not use the idea in any other applications, however, or define it ...
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.
Cournot's model argued that each firm should maximise its profit by selecting a quantity level and then adjusting price level to sell that quantity. The outcome of the model equilibrium involved firms pricing above marginal cost; hence, the competitive price.
The general process for obtaining a Nash equilibrium of a game using the best response functions is followed in order to discover a Nash equilibrium of Cournot's model for a specific cost function and demand function. A Nash Equilibrium of the Cournot model is a (,) such that
The Cournot equilibrium is reached when each firm operates on their reaction function with no incentive to deviate, as they have the best response based on the other firms output. [22] Within the game, firms reach the Nash equilibrium when the Cournot equilibrium is achieved. Equilibrium for Cournot quantity competition
However, some Cournot strategy profiles are sustained as Nash equilibria but can be eliminated as incredible threats (as described above) by applying the solution concept of subgame perfection. Indeed, it is the very thing that makes a Cournot strategy profile a Nash equilibrium in a Stackelberg game that prevents it from being subgame perfect.
In oligopoly theory, conjectural variation is the belief that one firm has an idea about the way its competitors may react if it varies its output or price. The firm forms a conjecture about the variation in the other firm's output that will accompany any change in its own output.