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October  2017, 4(4): 361-367. doi: 10.3934/jdg.2017019

A new perspective on the classical Cournot duopoly

Rabah Amir 1,, and  Igor V. Evstigneev 2,

1. 

Department of Economics, University of Iowa, Iowa City, IA 52242-1994, USA
2. 

Department of Economics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

* Corresponding author

Received  April 2017 Revised  September 2017 Published  September 2017

The paper provides new conditions for the existence, uniqueness, and symmetry of pure-strategy Nash equilibrium in the classical Cournot duopoly.

Keywords: Cournot duopoly, potential games, pure-strategy Nash equilibria, existence, uniqueness, symmetry.
Mathematics Subject Classification: Primary: 91A10; Secondary: 91A40, 91A80, 91B24.
Citation: Rabah Amir, Igor V. Evstigneev. A new perspective on the classical Cournot duopoly. Journal of Dynamics & Games, 2017, 4 (4) : 361-367. doi: 10.3934/jdg.2017019
References:
[1]

R. Amir, Cournot oligopoly and the theory of supermodular games, Games and Economic Behavior, 15 (1996), 132-138.  doi: 10.1006/game.1996.0062.  Google Scholar

[2]

R. Amir and V. Lambson, On the effects of entry in Cournot markets, Review of Economic Studies, 67 (2000), 235-254.  doi: 10.1016/S0022-0531(03)00002-4.  Google Scholar

[3]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Hachette Livre, Paris, 1838. Google Scholar

[4]

C. Ewerhart, Cournot games with bi-concave demand, Games and Economic Behavior, 85 (2014), 37-47.  doi: 10.1016/j.geb.2014.01.001.  Google Scholar

[5]

J. W. Friedman, Oligopoly and the Theory of Games, North-Holland, Amsterdam, 1977. Google Scholar

[6]

G. Gaudet and S. Salant, Uniqueness of Cournot equilibrium: New results from old methods, Review of Economic Studies, 58 (1991), 399-404.  doi: 10.2307/2297975.  Google Scholar

[7]

C. Kolstad and L. Mathiesen, Necessary and sufficient conditions for uniqueness of a Cournot equilibrium, Review of Economic Studies, 54 (1987), 681-690.  doi: 10.2307/2297489.  Google Scholar

[8]

M. McManus, Equilibrium, number and size in Cournot oligopoly, Yorkshire Bulletin of Economic and Social Research, 16 (1964), 68-75.  doi: 10.1111/j.1467-8586.1964.tb00517.x.  Google Scholar

[9]

D. Monderer and L.S. Shapley, Potential games, Games and Economic Behavior, 14 (1996), 124-143.  doi: 10.1006/game.1996.0044.  Google Scholar

[10]

W. Novshek, On the existence of Cournot equilibrium, Review of Economic Studies, 52 (1985), 85-98.  doi: 10.2307/2297471.  Google Scholar

[11]

J. Roberts and H. Sonnenschein, On the existence of Cournot equilibrium without concave profit functions, Journal of Economic Theory, 13 (1976), 85-98.  doi: 10.1016/0022-0531(76)90069-7.  Google Scholar

[12]

F. Szidarovszky and S. Yakowitz, On the existence of Cournot equilibrium, International Economic Review, 18 (1977), 787-789.  doi: 10.2307/2525963.  Google Scholar

[13]

A. Tarski, A lattice-theoretic fixed point theorem and its applications, Pacific Journal of Mathematics, 5 (1955), 285-309.  doi: 10.2140/pjm.1955.5.285.  Google Scholar

[14]

D. Topkis, Submodularity and Complementarity, Princeton University Press, Princeton, NJ., 1998.  Google Scholar

[15]

X. Vives, Oligopoly Pricing: Old Ideas and New Tools, MIT Press, Cambridge, MA., 1999. Google Scholar

show all references

References:
[1]

R. Amir, Cournot oligopoly and the theory of supermodular games, Games and Economic Behavior, 15 (1996), 132-138.  doi: 10.1006/game.1996.0062.  Google Scholar

[2]

R. Amir and V. Lambson, On the effects of entry in Cournot markets, Review of Economic Studies, 67 (2000), 235-254.  doi: 10.1016/S0022-0531(03)00002-4.  Google Scholar

[3]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Hachette Livre, Paris, 1838. Google Scholar

[4]

C. Ewerhart, Cournot games with bi-concave demand, Games and Economic Behavior, 85 (2014), 37-47.  doi: 10.1016/j.geb.2014.01.001.  Google Scholar

[5]

J. W. Friedman, Oligopoly and the Theory of Games, North-Holland, Amsterdam, 1977. Google Scholar

[6]

G. Gaudet and S. Salant, Uniqueness of Cournot equilibrium: New results from old methods, Review of Economic Studies, 58 (1991), 399-404.  doi: 10.2307/2297975.  Google Scholar

[7]

C. Kolstad and L. Mathiesen, Necessary and sufficient conditions for uniqueness of a Cournot equilibrium, Review of Economic Studies, 54 (1987), 681-690.  doi: 10.2307/2297489.  Google Scholar

[8]

M. McManus, Equilibrium, number and size in Cournot oligopoly, Yorkshire Bulletin of Economic and Social Research, 16 (1964), 68-75.  doi: 10.1111/j.1467-8586.1964.tb00517.x.  Google Scholar

[9]

D. Monderer and L.S. Shapley, Potential games, Games and Economic Behavior, 14 (1996), 124-143.  doi: 10.1006/game.1996.0044.  Google Scholar

[10]

W. Novshek, On the existence of Cournot equilibrium, Review of Economic Studies, 52 (1985), 85-98.  doi: 10.2307/2297471.  Google Scholar

[11]

J. Roberts and H. Sonnenschein, On the existence of Cournot equilibrium without concave profit functions, Journal of Economic Theory, 13 (1976), 85-98.  doi: 10.1016/0022-0531(76)90069-7.  Google Scholar

[12]

F. Szidarovszky and S. Yakowitz, On the existence of Cournot equilibrium, International Economic Review, 18 (1977), 787-789.  doi: 10.2307/2525963.  Google Scholar

[13]

A. Tarski, A lattice-theoretic fixed point theorem and its applications, Pacific Journal of Mathematics, 5 (1955), 285-309.  doi: 10.2140/pjm.1955.5.285.  Google Scholar

[14]

D. Topkis, Submodularity and Complementarity, Princeton University Press, Princeton, NJ., 1998.  Google Scholar

[15]

X. Vives, Oligopoly Pricing: Old Ideas and New Tools, MIT Press, Cambridge, MA., 1999. Google Scholar

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