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Atlantic Economic Journal

, Volume 27, Issue 3, pp 325–333 | Cite as

Cournot, Bertrand, and game theory: A further note

  • Robert W. Dimand
  • Mohammed H. I. Dore
Articles

Abstract

This note synthesizes the discussion on the role of Cournot and Bertrand in the analysis of duopoly by drawing on the history of the debate. We conclude that while Bertrand presented a critique of the mathematical economics of Cournot and stimulated the analysis of strategic choice in game theory, he did not present a duopoly model with price as a strategic variable, as opposed to Cournot's model with quantity. In fact, Cournot has both types of models. We show that Irving Fisher contributed to the myth about Bertrand's duopoly theory.

Keywords

Game Theory International Economic Public Finance Strategic Choice Mathematical Economic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bachelier, Louis. "Théorie de la spéculation,"Annales scientifiques de l'École Normale Superiéure, 1900, pp. 21–86; reprinted and translated by A. J. Bonness, in Paul Cootner, ed., asThe Random Character of Stock Market Prices, Cambridge, MA: MIT Press, 1964.Google Scholar
  2. Bertrand, Joseph. "Théorie Mathématique de la Richesse Sociale,"Journal des Savants, 67, 1883, pp. 499–508; translated by Margaret Chevaillier in Appendix to Jean Magnan de Bornier,History of Political Economy, 1992, and in M. Dimand and R. Dimand, eds.,The Foundations of Game Theory (Volumes I–III), Cheltenham, United Kingdom: Edward Elgar, 1997; reprinted and translated by James W. Friedman, in Andrew F. Daughety, ed., asCournot Oligopoly, Cambridge, United Kingdom: Cambridge University Press, 1988, pp. 73–81.Google Scholar
  3. Bertrand, Joseph.Calcul des probabilités, éléments de la théorie des probabilités, 3rd ed., Paris, France: Gauthier-Villars, 1889, 1924.Google Scholar
  4. Borel, Emile. "La théorie du jeu et les equations integrales a noyau symetrique gauche,"Comptes Rendus de l'Académie des Sciences, 173, 1924, pp. 1304–8; translated by L. J. Savage as "The Theory of Play and Integral Equations with Skew Symmetric Kernels,"Econometrica, 21, 1, 1953, pp. 97–100.Google Scholar
  5. Brems, Hans.Quantitative Economic Theory, New York, NY: John Wiley and Sons, 1968.Google Scholar
  6. Breton, Y. "Les économistes liberaux français et l'emploi des mathématiques en économiepolitique, 1800–1914,’`Oeconomia, 5, 1986, pp. 2–25.Google Scholar
  7. Cherriman, J. B., "Review of Cournot (1838),"Canadian Journal of Industry, Science and Art, 2, 1857, pp. 185–94; reprinted as an Appendix in R. W. Dimand, "Cournot, Bertrand, and Cherriman,"History of Political Economy, 27, 2, Fall 1995, pp. 563–78.Google Scholar
  8. Cournot, A. A.Recherches sur les Principes Mathématiques de la Théorie des Richesses, Paris, France: L. Hachette, 1838; reprinted with introduction and notes by Georges Lutfalla and text by L. Walras; J. Bertrand; V. Pareto, Paris, France: M. Rivere, 1938; translated by N. T. Bacon with introduction and notes by Irving Fisher, New York, NY: Macmillan, 1897, 1927; reprinted New York, NY: Augustus M. Kelley, 1960.Google Scholar
  9. Cournot, A. A.,Principles de la Théoire des Richesses, Paris, France: L. Hachette, 1863; reprinted Paris, France: J. Vrin, 1981.Google Scholar
  10. Daughety, Andrew F., ed. Introduction toCournot Oligopoly: Characterization and Applications, Cambridge, United Kingdom: Cambridge University Press, 1988, pp. 3–44.Google Scholar
  11. de Fontenay, R. "Review of Principles de la Théorie des Richesses by A. A. Cournot,"Journal des Économistes, 2, 43, August 1864, pp. 231–51.Google Scholar
  12. Dimand, Mary Ann; Dimand, Robert W.A History of Game Theory, Volume 1: From the Beginning to 1945, London, United Kingdom: Routledge, 1996.Google Scholar
  13. __; eds.The Foundations of Game Theory (Volumes I–III), Cheltenham, United Kingdom: Edward Elgar, 1997.Google Scholar
  14. Dimand, Robert W. "An Early Canadian Contribution to Mathematical Economics: J. B. Cherriman's 1857 Review of Cournot,"Canadian Journal of Economics, 21, 3, August 1988, pp. 610–16.Google Scholar
  15. __ "The Case of Brownian Motion: The Contribution of Bachelier,"British Journal for the History of Science, 26, 1993, pp. 233–4.Google Scholar
  16. __ "Cournot, Bertrand, and Cherriman,"History of Political Economy, 27, 3, Fall 1995, pp. 563–78.Google Scholar
  17. Dimand, Robert W.; Dimand, Mary Ann. "From Games of Pure Chance to Strategic Games: French Probabilists and Early Game Theory," In Christian Schmidt, ed.,Uncertainty in Economic Thought, Cheltenham, United Kingdom and Brookfield, VT: Edward Elgar, 1996, pp. 157–68.Google Scholar
  18. Ekelund, Robert B.; Hébert, Robert F. "Cournot and His Contemporaries: Is an Obituary the Only Bad Review?,"Southern Economic Journal, 57, 1, July 1990, pp. 139–49.Google Scholar
  19. Fisher, Irving. "Cournot and Mathematical Economics,"Quarterly Journal of Economics, 12, January 1898, pp. 119–38.Google Scholar
  20. __. "Cournot Forty Years Ago,"Econometrica, 6, 3, July 1938, pp. 198–202.Google Scholar
  21. Hutchison, T. W. A.,Review of Economic Doctrines 1870–1929, Oxford, United Kingdom: Clarendon Press, 1953.Google Scholar
  22. Leonard, Robert J. "Reading Cournot, Reading Nash: The Creation and Stabilisation of the Nash Equilibrium,"Economic Journal, 104, May 1994, pp. 492–511.Google Scholar
  23. Magnan de Bornier, Jean. "The ‘Cournot-Bertrand Debate’: A Historical Perspective,"History of Political Economy, 24, 3, Fall 1993, pp. 623–56.Google Scholar
  24. Morrison, Clarence C. "Cournot, Bertrand, and Modern Game Theory,"Atlantic Economic Journal, 26, 2, June 1998, pp. 172–4.Google Scholar
  25. Nash, John F., Jr.Essays on Game Theory, with introduction by Ken Binmore, Cheltenham, United Kingdom: Edward Elgar, 1996.Google Scholar
  26. Prekopa, Andras. "On the Development of Optimization Theory,"American Mathematical Monthly, 87, 7, 1980, pp. 527–42.Google Scholar
  27. Schumpeter, Joseph A. in Elizabeth B. Schumpeter, ed.,History of Economic Analysis, New York, NY: Oxford University Press, 1954.Google Scholar
  28. Spiegel, Henry W., ed.The Development of Economic Thought, New York, NY: John Wiley and Sons, 1952.Google Scholar
  29. Theocharis, Reghinos D. "A Lag in the Recognition of Cournot's Contribution to Economic Analysis,"Canadian Journal of Economics, 23, 4, November 1990, pp. 923–33.Google Scholar
  30. Walras, Léon.Théorie Mathématique de la Richesse Sociale, Lausanne, Switzerland: Corbaz, 1883.Google Scholar
  31. Zylberberg, Andre.L'Économie Mathématique en France 1870–1914, Paris, France:Economica, 1990.Google Scholar

Copyright information

© International Atlantic Economic Society 1999

Authors and Affiliations

  • Robert W. Dimand
    • 1
  • Mohammed H. I. Dore
    • 1
  1. 1.Brock UniversityCanada

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