| 11. |
- Agliari, Anna, et al.
(författare)
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Global bifurcations of basins in a triopoly game
- 2002
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 12:10, s. 2175-2207
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Tidskriftsartikel (refereegranskat)abstract
- A Cournot model based on bounded inverse demand function and constant marginal production costs is studied. The case of three producers is considered and the adjustment process reduces to a three-dimensional noninvertible map in the output of competitors. The analysis of the dynamical behavior of the map is performed by the "critical curve method", extended to the critical surfaces in 3D. By this method, we explain the different bifurcations in the basins of attraction and in the attracting sets. In particular, given the economic application, feasible trajectories are focused, starting from the simple situation of two identical producers and extending the results to the generic case.
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| 12. |
- Agliari, Anna, et al.
(författare)
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The dynamics of a triopoly Cournot game
- 2000
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 11:15, s. 2531-2560
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Tidskriftsartikel (refereegranskat)abstract
- This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic demand and constant marginal costs, one of the rare cases where the reaction functions can be derived in closed form. It focuses the case of three competitors, and so also extends the critical line method for non-invertible maps to the study of critical surfaces in 3D. By this method the various bifurcations of the attractors and their basins are studied. As a special case the restriction of the map to an invariant plane when two of the three firms are identical is focused.
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| 13. |
- Canovas, Jose S, et al.
(författare)
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Detecting Chaos in a Duopoly Model via Symbolic Dynamics
- 2010
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Ingår i: Discrete and continuous dynamical systems. Series B. - Springfield, USA : American Institute of Mathematical Sciences. - 1531-3492 .- 1553-524X. ; 13:2, s. 269-278
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with built-in capacity limits. When the firms cannot obtain positive profits they are assumed to choose small "stand-by" outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turnout more favorable. It is shown that the model provides chaotic behavior. In particular, the system has positive topological entropy and hence the map is chaotic in the Li-Yorke sense. Moreover, chaos is not only topological but also physically observable.
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| 14. |
- Gallegati, Mauro, et al.
(författare)
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Hicks’ trade cycle revisited : cycles and bifurcations
- 2003
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Ingår i: Mathematics and Computers in Simulation. - 0378-4754 .- 1872-7166. ; 63:6, s. 505-527
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Tidskriftsartikel (refereegranskat)abstract
- In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is needed to have non explosive outcome if the equilibrium point is an unstable focus. It will also be shown that when the fixed point is unstable the attracting set has a particular structure: It is a one-dimensional closed invariant curve, made up of a finite number of linear pieces, on which the dynamics are either periodic or quasi-periodic. The conditions under which the model produces periodic or quasi-periodic trajectories and the related bifurcations as a function of the main economic parameters are determined.
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| 15. |
- Panchuk, A., et al.
(författare)
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Dynamics of a durable commodity market involving trade at disequilibrium
- 2018
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Ingår i: Communications in nonlinear science & numerical simulation. - : ELSEVIER SCIENCE BV. - 1007-5704 .- 1878-7274. ; 58, s. 2-14
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Tidskriftsartikel (refereegranskat)abstract
- The present work considers a simple model of a durable commodity market involving two agents who trade stocks of two different types. Stock commodities, in contrast to flow commodities, remain on the market from period to period and, consequently, there is neither unique demand function nor unique supply function exists. We also set up exact conditions for trade at disequilibrium, the issue being usually neglected, though a fact of reality. The induced iterative system has infinite number of fixed points and path dependent dynamics. We show that a typical orbit is either attracted to one of the fixed points or eventually sticks at a no-trade point. For the latter the stock distribution always remains the same while the price displays periodic or chaotic oscillations. (C) 2017 Elsevier B.V. All rights reserved.
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| 16. |
- Panchuk, Anastasiia, et al.
(författare)
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Stability in a non-autonomous iterative system : an application to oligopoly
- 2009
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Ingår i: Computers and Mathematics with Applications. - Oxford : Pergamon Press. - 0898-1221 .- 1873-7668. ; 58:10, s. 2022-2034
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Tidskriftsartikel (refereegranskat)abstract
- This paper reconsiders the relation between oligopoly and perfect competition, more specifically the problem of emergent instability when the number of competitors increases, as pointed out by several authors. A process of mixed short and long run dynamics is set up. In the short run the competitors are subject to capacity limits due to fixed capital stocks, in the long run they may renew these stocks and so in the moments of reinvestment have access to a constant returns technology. The evolution of the system depends on the number of competitors, the interval between their entry on the market, and the durability of capital. The main result is a theorem showing that if capital has a durability of more periods than the spacing of reinvestment times among the firms, multiplied with their total number, then the system always contracts to the Cournot equilibrium state.
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| 17. |
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| 18. |
- Puu, Tönu, 1936-
(författare)
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A simplified model of spatiotemporal population dynamics.
- 1985
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Ingår i: Environment and planning A. - 0308-518X .- 1472-3409. ; 17:9, s. 263-269
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Tidskriftsartikel (refereegranskat)abstract
- This paper is an extension of the model of population growth and migration originally developed by H. Hotelling in 1921. This model consists of two ingredients, a logistic growth function and a linear spatial diffusion term. The author notes that the saturation population can be affected by the development of new technology and that improvements in transportation have increased the possibilities for migration. "Basic nonlinearities are introduced by use of a production technology with increasing-decreasing returns to scale. It is demonstrated how industrial takeoffs, population transitions, and agglomerative spatial patterns can emerge by changing the model parameters.
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| 19. |
- Puu, Tönu, 1936-
(författare)
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Bertrand oligopoly revisited
- 2001
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Ingår i: Discrete dynamics in nature and society. - 1026-0226 .- 1607-887X. ; 6:1, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- This paper reconsiders Bertrand duopoly and oligopoly in the spatial formulation due to Hotelling, 1929. The equilibrium configurations of price and location structure are considered, given elastic demand, and a full dynamics is formulated in order to check for stability of equilibrium and the possibilities of complex dynamics, such as occurs easily with Cournot oligopoly. The main discussion concerns Hotelling's original case of two sellers on a given interval, though results for different cases, such as three firms on a circle, and lattices in 2D are indicated.
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| 20. |
- 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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