Cournot, Bertrand, and Modern Game Theory

By Morrison, Clarence C. | Atlantic Economic Journal, June 1998 | Go to article overview

Cournot, Bertrand, and Modern Game Theory


Morrison, Clarence C., Atlantic Economic Journal


Introduction

In 1838, Augustin Cournot published his now famous Recherches sur les Principes Mathematiques de la Theorie des Richesses. In this small volume and with mathematical precision, Cournot explicitly set forth much of the modern day theory of competition, monopoly, and oligopoly. In 1883, J. Bertrand undertook a joint review of Cournot's book and Leon Walrus' Theorie Mathematique de la Richesse Sociale [1883] which had just appeared. In this review, Bertrand argued that Cournot's equilibrium for duopoly was not a true equilibrium because "whatever the common price adopted, if one of the owners, alone, reduces his price, he will, ignoring any minor exceptions, attract all of the buyers, and thus double his revenue if his rival lets him do so" [Bertrand, 1883].(1) It is now textbook-commonplace that, for homogeneous products, if each rival assumes that the other rival will let him do so, this type of rivalry would lead to the competitive result of price set equal to marginal cost.

As criticized by Bertrand, Cournot arrived at the equilibrium by assuming that each rival took the other rival's quantities as given and put his profit-maximizing quantity on the market. After stating each rival's profit function regarding the quantities that all rivals place on the market, Cournot partially differentiated each rival's profit function, with respect to that rival's own quantity and equated each of the resulting expressions to zero.(2)

For the duopoly case, Cournot plotted the resulting equations in rectangular coordinates and pointed out that it is evident that an equilibrium can only be established where the curves intersect [1838, p. 81]. Figure 2 gives the plotted curves and illustrates the sequential algorithm for finding this equilibrium.(3) In the more general case of n proprietors, equilibrium is given by the simultaneous solution of the equations [pp. 84-5].

In plotting the respective first-order conditions (for maximizing the profit of each rival given the other rival's quantities), Cournot implicitly solved for functions giving the reactions of each rival to the other rival's strategies. In modern game theory, these functions are called best-response functions. Where the curves intersect (for the two-dimensional case or for the simultaneous solution of Cournot's equations in general), it turns out that all of the rivals' conjectures about strategies are actually correct. No rival changes his strategy in reaction to the observed strategies of the other rivals. J. F. Nash [1950, 1951] extended this basic idea to noncooperative games in general and provided sufficient conditions for such equilibria to exist. In modern game theory, best-response solutions with mutually correct conjectures are referred to as Nash equilibria.

The above summary is provided as background for discussing the nomenclature that has evolved in the application of modern game theory to the analysis of market structures. Almost without exception in current industrial organization literature, market rivalry involving quantity strategies is referred to as Cournot competition and market rivalry involving price strategies is referred to as Bertrand competition. The corresponding equilibria are referred to as Cournot equilibria and Bertrand equilibria. Where the equilibria are best-response solutions with mutually correct conjectures, they are described as being Cournot-Nash and Bertrand-Nash, respectively. In light of the summary, this would seem to be convenient nomenclature that is firmly rooted in the historical evolution of economic ideas. In fact, this nomenclature actually does great violence to the history of economic thought.

What has been forgotten (or never learned) is that, in his 1838 classic, Cournot symmetrically treated both quantity rivalry and price rivalry (in the sense of analyzing both best-response functions with equilibrium given where conjectures are mutually correct). The most glaring example of the problem arises in the analysis of oligopoly with differentiated products. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • A full archive of books and articles related to this one
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Cournot, Bertrand, and Modern Game Theory
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

    Already a member? Log in now.