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A probability criterion for zero-sum stochastic 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. |
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