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Conjectural variation


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. For example, in the classic Cournot model of oligopoly, it is assumed that each firm treats the output of the other firms as given when it chooses its output. This is sometimes called the "Nash conjecture" as it underlies the standard Nash equilibrium concept. However, alternative assumptions can be made. Suppose you have two firms producing the same good, so that the industry price is determined by the combined output of the two firms (think of the water duopoly in Cournot's original 1838 account). Now suppose that each firm has what is called the "Bertrand Conjecture" of −1. This means that if firm A increases its output, it conjectures that firm B will reduce its output to exactly offset firm A's increase, so that total output and hence price remains unchanged. With the Bertrand Conjecture, the firms act as if they believe that the market price is unaffected by their own output, because each firm believes that the other firm will adjust its output so that total output will be constant. At the other extreme is the Joint-Profit maximizing conjecture of +1. In this case each firm believes that the other will imitate exactly any change in output it makes, which leads (with constant marginal cost) to the firms behaving like a single monopoly supplier.

The notion of conjectures has maintained a long history in the Industrial Organization theory ever since the introduction of Conjectural Variations Equilibria by Arthur Bowley in 1924 and Ragnar Frisch (1933) (a useful summary of the history is provided by Giacoli). Not only are conjectural variations (henceforth CV) models able to capture a range of behavioral outcomes – from competitive to cooperative, but also they have one parameter which has a simple economic interpretation. CV models have also been found quite useful in the empirical analysis of firm behavior in the sense that they provide a more general description of firms behavior than the standard Nash equilibrium.

As Stephen Martin has argued:

There is every reason to believe that oligopolists in different markets interact in different ways, and it is useful to have models that can capture a wide range of such interactions. Conjectural oligopoly models, in any event, have been more useful than game-theoretic oligopoly models in guiding the specification of empirical research in industrial economics.


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