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The Classical Cournot Model

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Abstract

In this chapter we will introduce the classical Cournot model, which is also known as the single-product quantity setting oligopoly model without product differentiation. In the first section of the chapter the Cournot model will be discussed as an N-firm static game and the best responses of the firms and the equilibria will be determined in a series of examples, many of which will be built upon in developing the ideas in subsequent chapters. Section 1.2 introduces the dynamic adjustment processes via which we shall assume that firms adjust output over time. We will in particular discuss expectation formation processes and adaptive adjustments and gradient adjustments. The final section will illustrate by simple examples the complexity of the dynamics that can arise in these models due to certain nonlinear features to be described below. The fundamental techniques for the global analysis of the dynamics of such models will be explained in Sect. 1.3.

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Notes

  1. 1.

    In the game theory context the profit functions are usually called the payoff functions, and the firms are called the players. We will occasionally make use of these terms throughout this book.

  2. 2.

    This interpretation is based on the fact that the condition is satisfied if − ek (k = 1, 2) does not get too close to B.

  3. 3.

    See Agliari et al. (2005, 2006), Agliari (2006) and Matsumoto and Serizawa (2007).

  4. 4.

    Consider a one-dimensional, continuously differentiable map g(y). If g′(y) > 0, then for x < y, it follows that g(x) < g(y). If, on the other hand, g′(y) < 0, the orientation is reversed. Obviously, the change of signs occurs exactly at the point where the derivative vanishes.

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Author information

Authors and Affiliations

  1. Dipartimento di Economia e Metodi Quantitativi (DEMQ), Università di Urbino “Carlo Bo”, via Saffi n.42, I-61029, Urbino, Italy

    Professor Gian-Italo Bischi

  2. School of Finance and Economics, University of Technology, Sydney, 123, Broadway, NSW, 2007, Australia

    Professor Carl Chiarella

  3. University of Graz Institute of Organization and Economics of Institutions University of Graz, Universitätsstraße 15/E4, A-8010, Graz, Austria

    Professor Michael Kopel

  4. Systems and Industrial Engineering Department, University of Arizona, Tucson, AZ, 85721-0020, USA

    Professor Ferenc Szidarovszky

Authors
  1. Professor Gian-Italo Bischi
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  2. Professor Carl Chiarella
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  3. Professor Michael Kopel
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  4. Professor Ferenc Szidarovszky
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Corresponding authors

Correspondence to Gian-Italo Bischi , Carl Chiarella , Michael Kopel or Ferenc Szidarovszky .

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Bischi, GI., Chiarella, C., Kopel, M., Szidarovszky, F. (2010). The Classical Cournot Model. In: Nonlinear Oligopolies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02106-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-02106-0_1

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