We study a heterogeneous duopolistic Cournotian game, in which the firms, producing a homogeneous good, have reduced rationality and respectively adopt a “Local Monopolistic Approximation” (LMA) and a gradient-based approach with endogenous reactivity, in an economy characterized by isoelastic demand function and linear total costs. We give conditions on reactivity and marginal costs under which the solution converges to the Cournot–Nash equilibrium. Moreover, we compare the stability regions of the proposed oligopoly to a similar one, in which the LMA firm is replaced by a best response firm, which is more rational than the LMA firm. We show that, depending on costs ratio, the equilibrium can lose its stability in two different ways, through both a flip and a Neimark–Sacker bifurcation. We show that the nonlinear, noninvertible map describing the model can give rise to several coexisting stable attractors (multistability). We analytically investigate the shape of the basins of attractions, in particular proving the existence of regions known in the literature as lobes.

Cavalli, F., Naimzada, A., Tramontana, F., Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity, <<COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION>>, 2015; 23 (1-3): 245-262. [doi:10.1016/j.cnsns.2014.11.013] [http://hdl.handle.net/10807/67380]

Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity

Cavalli, Fausto;Tramontana, Fabio
2015

Abstract

We study a heterogeneous duopolistic Cournotian game, in which the firms, producing a homogeneous good, have reduced rationality and respectively adopt a “Local Monopolistic Approximation” (LMA) and a gradient-based approach with endogenous reactivity, in an economy characterized by isoelastic demand function and linear total costs. We give conditions on reactivity and marginal costs under which the solution converges to the Cournot–Nash equilibrium. Moreover, we compare the stability regions of the proposed oligopoly to a similar one, in which the LMA firm is replaced by a best response firm, which is more rational than the LMA firm. We show that, depending on costs ratio, the equilibrium can lose its stability in two different ways, through both a flip and a Neimark–Sacker bifurcation. We show that the nonlinear, noninvertible map describing the model can give rise to several coexisting stable attractors (multistability). We analytically investigate the shape of the basins of attractions, in particular proving the existence of regions known in the literature as lobes.
Inglese
Cavalli, F., Naimzada, A., Tramontana, F., Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity, <<COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION>>, 2015; 23 (1-3): 245-262. [doi:10.1016/j.cnsns.2014.11.013] [http://hdl.handle.net/10807/67380]
File in questo prodotto:
File Dimensione Formato  
CavNaiTra CNSNS15.pdf

non disponibili

Tipologia file ?: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 2.94 MB
Formato Unknown
2.94 MB Unknown   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/67380
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 68
  • ???jsp.display-item.citation.isi??? 66
social impact