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Rational expectations and the Cournot-Theocharis problem. (English) Zbl 1152.91328

Summary: In dynamic models in economics, often “rational expectations” are assumed. These are meant to show that the agents can correctly foresee the result of their own and the other agents’ actions. In this paper, it is shown that this cannot happen in a simple oligopoly model with a linear demand function and constant marginal costs. “Naive expectations,” that is, where each agent assumes the other agents to retain their previous period action, are shown to result in a 2-period cycle. However, adapting to the observed periodicity always doubles the actual resulting periodicity. In general, it is impossible for the agents to learn any periodicity except the trivial case of a fixed point. This makes the whole idea of “rational expectations” untenable in Cournot oligopoly models.

MSC:

91A10 Noncooperative games
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References:

[1] J. Cánovas, T. Puu, and M. Ruiz, “The Cournot-theocharis problem revisited,” to appear in Chaos, Solutions, and Fractals.
[2] A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Hachette, Paris, 1838. · Zbl 0174.51801
[3] T. F. Palander, “Konkurrens och marknadsjämvikt vid duopol och oligopol,” Ekonomisk Tidskrift, vol. 41, pp. 124-145, 222-250, 1939.
[4] T. F. Palander, “Instability in competition between two sellers,” Abstracts of Papers Presented at the Research Conference on Economics and Statistics held by the Cowles Commission at Colorado College, Colorado College, General Series no. 208, Studies Series no. 21, 1936.
[5] R. D. Theocharis, “On the stability of the Cournot solution on the oligopoly problem,” Review of Economic Studies, vol. 27, pp. 133-134, 1959.
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