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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 ...
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.
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.
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 Nash Equilibrium in the Bertrand model is the mutual best response; an equilibrium where neither firm has an incentive to deviate from it. As illustrated in the Diagram 2, the Bertrand-Nash equilibrium occurs when the best response function for both firm's intersects at the point, where P 1 N = P 2 N = M C {\displaystyle P_{1}^{N}=P_{2}^{N ...
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 ...
Non-cooperative games have a long history, beginning with Cournot's duopoly model. A 1994 Nobel Laureate for Economic Sciences, John Nash, [7] proved a general-existence theorem for non-cooperative games, which moves beyond simple zero-sum games. This theory was generalized by Vickrey (1961) to deal with the unobservable value of each buyer.
If the leader played a Stackelberg action, (it believes) that the follower will play Cournot. Hence it is non-optimal for the leader to play Stackelberg. In fact, its best response (by the definition of Cournot equilibrium) is to play Cournot quantity. Once it has done this, the best response of the follower is to play Cournot.