-
Previous Article
A probability criterion for zero-sum stochastic games
- JDG Home
- This Issue
-
Next Article
Nonlinear dynamics from discrete time two-player status-seeking games
A new perspective on the classical Cournot duopoly
| 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 |
The paper provides new conditions for the existence, uniqueness, and symmetry of pure-strategy Nash equilibrium in the classical Cournot duopoly.
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. |
| [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. |
| [3] |
A. Cournot,
Recherches sur les Principes Mathématiques de la Théorie des Richesses, Hachette Livre, Paris, 1838. |
| [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. |
| [5] |
J. W. Friedman,
Oligopoly and the Theory of Games, North-Holland, Amsterdam, 1977. |
| [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. |
| [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. |
| [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. |
| [9] |
D. Monderer and L.S. Shapley,
Potential games, Games and Economic Behavior, 14 (1996), 124-143.
doi: 10.1006/game.1996.0044. |
| [10] |
W. Novshek,
On the existence of Cournot equilibrium, Review of Economic Studies, 52 (1985), 85-98.
doi: 10.2307/2297471. |
| [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. |
| [12] |
F. Szidarovszky and S. Yakowitz,
On the existence of Cournot equilibrium, International Economic Review, 18 (1977), 787-789.
doi: 10.2307/2525963. |
| [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. |
| [14] |
D. Topkis,
Submodularity and Complementarity, Princeton University Press, Princeton, NJ., 1998. |
| [15] |
X. Vives,
Oligopoly Pricing: Old Ideas and New Tools, MIT Press, Cambridge, MA., 1999. |
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. |
| [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. |
| [3] |
A. Cournot,
Recherches sur les Principes Mathématiques de la Théorie des Richesses, Hachette Livre, Paris, 1838. |
| [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. |
| [5] |
J. W. Friedman,
Oligopoly and the Theory of Games, North-Holland, Amsterdam, 1977. |
| [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. |
| [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. |
| [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. |
| [9] |
D. Monderer and L.S. Shapley,
Potential games, Games and Economic Behavior, 14 (1996), 124-143.
doi: 10.1006/game.1996.0044. |
| [10] |
W. Novshek,
On the existence of Cournot equilibrium, Review of Economic Studies, 52 (1985), 85-98.
doi: 10.2307/2297471. |
| [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. |
| [12] |
F. Szidarovszky and S. Yakowitz,
On the existence of Cournot equilibrium, International Economic Review, 18 (1977), 787-789.
doi: 10.2307/2525963. |
| [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. |
| [14] |
D. Topkis,
Submodularity and Complementarity, Princeton University Press, Princeton, NJ., 1998. |
| [15] |
X. Vives,
Oligopoly Pricing: Old Ideas and New Tools, MIT Press, Cambridge, MA., 1999. |
| [1] |
Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics and Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 |
| [2] |
Athanasios Kehagias. A note on the Nash equilibria of some multi-player reachability/safety games. Journal of Dynamics and Games, 2022, 9 (1) : 117-122. doi: 10.3934/jdg.2021028 |
| [3] |
Josu Doncel, Nicolas Gast, Bruno Gaujal. Discrete mean field games: Existence of equilibria and convergence. Journal of Dynamics and Games, 2019, 6 (3) : 221-239. doi: 10.3934/jdg.2019016 |
| [4] |
Alejandra Fonseca-Morales, Onésimo Hernández-Lerma. A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models†. Journal of Dynamics and Games, 2017, 4 (3) : 195-203. doi: 10.3934/jdg.2017012 |
| [5] |
Fengjun Wang, Qingling Zhang, Bin Li, Wanquan Liu. Optimal investment strategy on advertisement in duopoly. Journal of Industrial and Management Optimization, 2016, 12 (2) : 625-636. doi: 10.3934/jimo.2016.12.625 |
| [6] |
Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics and Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537 |
| [7] |
Iraklis Kollias, Elias Camouzis, John Leventides. Global analysis of solutions on the Cournot-Theocharis duopoly with variable marginal costs. Journal of Dynamics and Games, 2017, 4 (1) : 25-39. doi: 10.3934/jdg.2017002 |
| [8] |
Akio Matsumoto, Ferenc Szidarovszky. Stability switching and its directions in cournot duopoly game with three delays. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5905-5923. doi: 10.3934/dcdsb.2021069 |
| [9] |
Carlos Hervés-Beloso, Emma Moreno-García. Market games and walrasian equilibria. Journal of Dynamics and Games, 2020, 7 (1) : 65-77. doi: 10.3934/jdg.2020004 |
| [10] |
Zahra Gambarova, Dionysius Glycopantis. On two-player games with pure strategies on intervals $ [a, \; b] $ and comparisons with the two-player, two-strategy matrix case. Journal of Dynamics and Games, 2022, 9 (3) : 299-322. doi: 10.3934/jdg.2022015 |
| [11] |
Xiaolin Xu, Xiaoqiang Cai. Price and delivery-time competition of perishable products: Existence and uniqueness of Nash equilibrium. Journal of Industrial and Management Optimization, 2008, 4 (4) : 843-859. doi: 10.3934/jimo.2008.4.843 |
| [12] |
Mingxia Li, Kebing Chen, Shengbin Wang. Retail outsourcing strategy in Cournot & Bertrand retail competitions with economies of scale. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021194 |
| [13] |
Sylvain Sorin, Cheng Wan. Finite composite games: Equilibria and dynamics. Journal of Dynamics and Games, 2016, 3 (1) : 101-120. doi: 10.3934/jdg.2016005 |
| [14] |
Bin Zhou, Hailin Sun. Two-stage stochastic variational inequalities for Cournot-Nash equilibrium with risk-averse players under uncertainty. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 521-535. doi: 10.3934/naco.2020049 |
| [15] |
Margarida Carvalho, João Pedro Pedroso, João Saraiva. Electricity day-ahead markets: Computation of Nash equilibria. Journal of Industrial and Management Optimization, 2015, 11 (3) : 985-998. doi: 10.3934/jimo.2015.11.985 |
| [16] |
Lesia V. Baranovska. Pursuit differential-difference games with pure time-lag. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1021-1031. doi: 10.3934/dcdsb.2019004 |
| [17] |
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 and Related Models, 2008, 1 (4) : 619-639. doi: 10.3934/krm.2008.1.619 |
| [18] |
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 |
| [19] |
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 |
| [20] |
Orlando Lopes. Uniqueness and radial symmetry of minimizers for a nonlocal variational problem. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2265-2282. doi: 10.3934/cpaa.2019102 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]