Asymptotic relations in Cournot's game

Guerrazzi, Marco (2012): Asymptotic relations in Cournot's game.

Abstract

In this note, I derive the asymptotic relation verified by oligopolists' iso-profit curves within Cournot's game. Thereafter, I provide an economic rationale for such a mathematical relation. The results of this exploration suggest that for each firm the asymptotes of the iso-profit curves convey the boundaries beyond which output competitors become net purchasers of the good supplied in the market.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cournot's Game; Nash Equilibrium; Asymptotes
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Bertrand, J. (1883), Revue de la Theorie Mathematique de la Richesse Sociale et des Recherches sur les Principles Mathematiques de la Theorie des Richesses, Journal des Savants, pp. 499-508.

Cournot A. (1838), Recherces sur les Principes Mathematiques de la Theorie de la Richesse. Paris: L. Hachette.

Guerrazzi M. (2012), On Involuntary Unemployment: Notes on Efficiency-Wage Competition, MPRA Paper, No. 38140.

Hahn F.H. (1987), On Involuntary Unemployment, Economic Journal, Supplement: Conference Papers, pp. 1-16.

Kopel M. (1996), Simple and Complex Adjustment Dynamics in Cournot Duopoly Models, Chaos, Solitons & Fractals, Vol. 7, No. 12, pp. 2031-2048.

Mas-Colell A., M. D. Whinston and J.R. Green (1995), Microeconomic Theory, New York: Oxford University Press.

Mayer T. (2000), Spatial Cournot Competition and Heterogeneous Production Costs Across Locations, Regional Science and Urban Economics, Vol. 30, No. 3, pp. 325-352.

Sing N. and X. Vives (1984), Price and Quantity Competition in a Differentiated Duopoly, RAND Journal of Economics, Vol. 15, No. 4, pp. 546-554.

Varian H.R. (1992), Microeconomic Analysis, 3rd Edition, New York: W.W. Norton & Company.