Abstract
In this paper, a Cournot oligopoly with isoelastic demand function and constant marginal cost is considered. The local stability conditions of the Cournot equilibrium are determined for four models with different decision mechanisms. In the first model, firms adjust their outputs using the best reply response with naive expectations. The second model is a generalization of the first one, where firms have adaptive expectations. Meanwhile, the third and fourth models adopt the bounded rationality and local monopolistic approximation, respectively. The results show that, in the case of identical firms, the Cournot equilibrium is always stable when the firms adopt the local monopolistic approximation mechanism.
Highlights
One of the key features which define a market structure is the number of firms in it
The theory of perfect competition states that as the number of firms in a market increases, the equilibrium of the market becomes stable and the market becomes perfectly competitive. This theory is at odds with the results presented in a seminal paper by Theocharis [6], which shows that equilibrium in a linear Cournot oligopoly with naive expectation and discrete time scale becomes unstable when there are more than three firms
Zhang and Gao [14] showed that the stability region of equilibrium in a Cournot oligopoly with quadratic cost function can be enlarged if the firms adopt local monopolistic approximation (LMA) as their decision mechanism
Summary
One of the key features which define a market structure is the number of firms in it. By using adaptive instead of naive expectation in a linear Cournot oligopoly, the equilibrium remains stable when the number of firms increases, provided that the adaptive adjustment is small Their results show that when four firms differentially adopt a naive expectation, adaptive expectation, bounded rationality, or LMA, the equilibrium is still locally stable.
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