| 1. |
|
|
| 2. |
|
|
| 3. |
- Agliari, Anna, et al.
(författare)
-
Global Bifurcations in Duopoly when the Cournot Point is Destabilized through a Subcritical Neimark Bifurcation
- 2003
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.
|
|
| 4. |
|
|
| 5. |
- Agliari, Anna, et al.
(författare)
-
Global bifurcations of basins in a triopoly game
- 2002
-
Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 12:10, s. 2175-2207
-
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.
|
|
| 6. |
- Agliari, Anna, et al.
(författare)
-
The dynamics of a triopoly Cournot game
- 2000
-
Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 11:15, s. 2531-2560
-
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.
|
|
| 7. |
|
|
| 8. |
- Canovas, Jose S, et al.
(författare)
-
Detecting Chaos in a Duopoly Model via Symbolic Dynamics
- 2010
-
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
-
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.
|
|
| 9. |
- Cánovas, J.S., et al.
(författare)
-
On the dynamics of a piecewise linear oligopoly model with capacity limits and reinvestment periods
- 2011
-
Ingår i: Nonlinear economic dynamics. - : Nova Science Publishers, Inc.. - 9781616687885 ; , s. 237-257
-
Bokkapitel (refereegranskat)abstract
- In this chapter we study the stability problem for an oligopoly market when the number of competitors grows. It has been pointed out that Cournot oligopoly is destabilized when the number of competitors grows beyond a very small number. However, all such studies concerned models with firms facing constant marginal costs. If one is interested in the question whether a Cournot equilibrium smoothly transforms into a perfect competition equilibrium when the number of competitors grows, the instability pointed out is neither surprising nor very relevant. In the competitive market we assume many small firms, whereas in the oligopoly there are few big firms. A firm with constant marginal costs is potentially infinitely large. So, to take this in consideration, we introduce capacity limits due to fixed amounts of capital which only occasionally are changed due to replacements of worn out capital. We find that the Cournot equilibrium destabilizes depending on the number of firms, but also on the way they choose the investment periods. Anyway, the oligopoly market becomes more complex when the number of firms increases.
|
|
| 10. |
- Gallegati, Mauro, et al.
(författare)
-
Hicks’ trade cycle revisited : cycles and bifurcations
- 2003
-
Ingår i: Mathematics and Computers in Simulation. - 0378-4754 .- 1872-7166. ; 63:6, s. 505-527
-
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.
|
|
