American Institute of Mathematical Sciences

Advanced
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

[1]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006
[2]

Josu Doncel, Nicolas Gast, Bruno Gaujal. Discrete mean field games: Existence of equilibria and convergence. Journal of Dynamics & Games, 2019, 6 (3) : 221-239. doi: 10.3934/jdg.2019016
[3]

Fengjun Wang, Qingling Zhang, Bin Li, Wanquan Liu. Optimal investment strategy on advertisement in duopoly. Journal of Industrial & Management Optimization, 2016, 12 (2) : 625-636. doi: 10.3934/jimo.2016.12.625
[4]

Alejandra Fonseca-Morales, Onésimo Hernández-Lerma. A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models†. Journal of Dynamics & Games, 2017, 4 (3) : 195-203. doi: 10.3934/jdg.2017012
[5]

Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics & Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537
[6]

Iraklis Kollias, Elias Camouzis, John Leventides. Global analysis of solutions on the Cournot-Theocharis duopoly with variable marginal costs. Journal of Dynamics & Games, 2017, 4 (1) : 25-39. doi: 10.3934/jdg.2017002
[7]

Akio Matsumoto, Ferenc Szidarovszky. Stability switching and its directions in cournot duopoly game with three delays. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021069
[8]

Carlos Hervés-Beloso, Emma Moreno-García. Market games and walrasian equilibria. Journal of Dynamics & Games, 2020, 7 (1) : 65-77. doi: 10.3934/jdg.2020004
[9]

Xiaolin Xu, Xiaoqiang Cai. Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial & Management Optimization, 2008, 4 (4) : 843-859. doi: 10.3934/jimo.2008.4.843
[10]

Sylvain Sorin, Cheng Wan. Finite composite games: Equilibria and dynamics. Journal of Dynamics & Games, 2016, 3 (1) : 101-120. doi: 10.3934/jdg.2016005
[11]

Bin Zhou, Hailin Sun. Two-stage stochastic variational inequalities for Cournot-Nash equilibrium with risk-averse players under uncertainty. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 521-535. doi: 10.3934/naco.2020049
[12]

Lesia V. Baranovska. Pursuit differential-difference games with pure time-lag. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1021-1031. doi: 10.3934/dcdsb.2019004
[13]

Margarida Carvalho, João Pedro Pedroso, João Saraiva. Electricity day-ahead markets: Computation of Nash equilibria. Journal of Industrial & Management Optimization, 2015, 11 (3) : 985-998. doi: 10.3934/jimo.2015.11.985
[14]

Claudia Negulescu, Anne Nouri, Philippe Ghendrih, Yanick Sarazin. Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics. Kinetic & Related Models, 2008, 1 (4) : 619-639. doi: 10.3934/krm.2008.1.619
[15]

Dean A. Carlson. Finding open-loop Nash equilibrium for variational games. Conference Publications, 2005, 2005 (Special) : 153-163. doi: 10.3934/proc.2005.2005.153
[16]

Matt Barker. From mean field games to the best reply strategy in a stochastic framework. Journal of Dynamics & Games, 2019, 6 (4) : 291-314. doi: 10.3934/jdg.2019020
[17]

Xue-Yan Wu, Zhi-Ping Fan, Bing-Bing Cao. Cost-sharing strategy for carbon emission reduction and sales effort: A nash game with government subsidy. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1999-2027. doi: 10.3934/jimo.2019040
[18]

Jeremias Epperlein, Stefan Siegmund, Petr Stehlík, Vladimír  Švígler. Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 803-813. doi: 10.3934/dcdsb.2016.21.803
[19]

Beatris A. Escobedo-Trujillo. Discount-sensitive equilibria in zero-sum stochastic differential games. Journal of Dynamics & Games, 2016, 3 (1) : 25-50. doi: 10.3934/jdg.2016002
[20]

James Montaldi. Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry. Journal of Geometric Mechanics, 2014, 6 (2) : 237-260. doi: 10.3934/jgm.2014.6.237

 Impact Factor: 

Tools

Metrics

  • PDF downloads (134)
  • HTML views (204)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences