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Role of reinvestment in a competitive market

Jose S. Cánovas (), Anastasiia Panchuk () and Tonu Puu ()
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Jose S. Cánovas: Universidad Polit Ì ecnica de Cartagena, Departamento de Matematica Aplicada y Estad Ì Ä±stica
Anastasiia Panchuk: nstitute of Mathematics, National Academy of Sciences of Ukraine
Tonu Puu: CERUM, Umea University, SE-90187 Umea, Sweden

No 12, Gecomplexity Discussion Paper Series from Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation"

Abstract: In the present work we study asymptotic dynamics of a multi-dimensional piecewise smooth map which models an oligopoly market where competitors use adaptive scheme for reaction choice. Each competitor also defines the moment for renewing the capital equipment depending on how intensively the latter is used. Namely, the larger output is produced, the quicker the capital exhausts. It is shown then that the asymptotic dynamics of the map is rather sensitive to initial conditions, which leads to coexistence of different metric attractors. We also investigate stability of trajectories representing Cournot equilibria, which in this case are not fixed but periodic points. In particular, it is shown that several such Cournot equilibria, belonging to different invariant manifolds, may coexist some of them being locally asymptotically stable and some being unstable.

Keywords: multidimensional piecewise smooth map; coexisting metric attractors; oligopoly market model; Cournot equilibrium stability (search for similar items in EconPapers)
JEL-codes: C61 C62 D41 D43 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2015-04, Revised 2015-04
New Economics Papers: this item is included in nep-com
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http://www.gecomplexity-cost.eu/repec/cst/wpaper/geco_dp_12.pdf First version, 2015 (application/pdf)

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