| 1. |
- Puu, Tönu, 1936-, et al.
(författare)
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Can Bertrand and Cournot oligopolies be combined?
- 2019
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 125, s. 97-107
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Tidskriftsartikel (refereegranskat)abstract
- There have been some recent attempts to combine Cournot and Bertrand duopolies in one single model. Unfortunately, these attempts do not work. A commodity cannot be homogenous and non-homogenous at the same time. It is always the consumers, who decide whether they perceive competing products as identical or as different brands for which they are willing to pay different prices. There is, of course, nothing that forbids the coexistence of both such consumer groups. Neither is there any obstacle for the competing sellers to sell to both markets. Then we only need an old idea from economic theory, i.e., price discrimination, to rectify the logic. By this the challenging combination idea comes on a stable footing. The model also results in some interesting mathematical facts, such as mulistability and coexistence of attractors.
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| 2. |
- Tramontana, Fabio, et al.
(författare)
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Cournot duopoly when the competitors operate multiple production plants
- 2009
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Ingår i: Journal of Economic Dynamics and Control. - : Elsevier BV. - 0165-1889 .- 1879-1743. ; 33:1, s. 250-265
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Tidskriftsartikel (refereegranskat)abstract
- This article considers a Cournot duopoly under an isoelastic demand function and cost functions with built-in capacity limits. The special feature is that each firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so each has three cost options, the third being to run both plants, dividing the load according to the principle of equal marginal costs. As a consequence, the marginal cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, may also consist of disjoint pieces. This is reflected in a particular bifurcation structure, due to border-collision bifurcations and to particular basin boundaries, related to the discontinuities. It is shown that stable cycles may coexist, and the non-existence of unstable cycles constitutes a new property. We also compare the coexistent short periodic solutions in terms of the resulting real profits.
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| 3. |
- Tramontana, Fabio, et al.
(författare)
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Global bifurcations in a piecewise-smooth Cournot duopoly game
- 2010
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Ingår i: Chaos, Solitons & Fractals. - Oxford : Pergamon-Elsevier Science Ltd. - 0960-0779 .- 1873-2887. ; 43:1-2, s. 15-24
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Tidskriftsartikel (refereegranskat)abstract
- The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu [2]. The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist. (C) 2010 Elsevier Ltd. All rights reserved.
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| 4. |
- Tramontana, Fabio, et al.
(författare)
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Mathematical properties of a discontinuous Cournot-Stackelberg model
- 2011
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 44:1-3, s. 58-70
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Tidskriftsartikel (refereegranskat)abstract
- The object of this work is to perform the global analysis of a recent duopoly model which couples the two points of view of Cournot and Stackelberg [17,18]. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigated as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which differ significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period.
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| 5. |
- Tramontana, Fabio, et al.
(författare)
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New properties of the Cournot duopoly with isoelastic demand and constant unit costs
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu (1991). The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Shacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties di¤er significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.
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