2013, 2013(special): 61-68. doi: 10.3934/proc.2013.2013.61

R&d dynamics

1. 

FCUP, University of Porto, Portugal, Portugal

2. 

LIAAD-INESC TEC Porto LA, Portugal, Portugal

Received  September 2012 Published  November 2013

We study a Cournot duopoly model using Ferreira-Oliveira-Pinto's R&D investment function. We find the multiple perfect Nash equilibria and we analyse the economical relevant quantities like output levels, prices, consumer surplus, profits and welfare.
Citation: J. Becker, M. Ferreira, B.M.P.M. Oliveira, A.A. Pinto. R&d dynamics. Conference Publications, 2013, 2013 (special) : 61-68. doi: 10.3934/proc.2013.2013.61
References:
[1]

C. d'Aspremont and A. Jacquemin, Cooperative and noncooperative R$&$D in duopoly with spillovers,, In, 78 (1988), 1133.   Google Scholar

[2]

J. A. Brander and B. J. Spencer, Strategic commitment with R$&$D: The symmetric case,, In, 14 (1983), 225.   Google Scholar

[3]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses,, Paris, (1838).   Google Scholar

[4]

F. A. Ferreira, F. Ferreira, M. Ferreira and A. A. Pinto, "Quantity Competition in a Differentiated Duopoly. Intelligent Engineering Systems and Computational Cybernetics,", Springer Netherlands, (2008).   Google Scholar

[5]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Patents in new technologies,, In, 15 (2009), 1135.   Google Scholar

[6]

M. Ferreira, I. F. Figueiredo, B. M. P. M. Oliveira and A. A. Pinto, Strategic optimization in R&D Investment,, In, (2011).   Google Scholar

[7]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Piecewise R&D Dynamics on costs,, In, 44 (2010), 29.   Google Scholar

[8]

A. A. Pinto, B. Oliveira, F. A. Ferreira and M. Ferreira, "Investing to Survive in a Duopoly Model. Intelligent Engineering Systems and Computational Cybernetics,", Springer Netherlands, (2008).   Google Scholar

[9]

L. Ruff,., Research and technological progress in a Cournot economy,, In, 1 (1969), 397.   Google Scholar

[10]

J. Tirole, "The Theory of Industrial Organization,", MIT Press, (1988).   Google Scholar

[11]

N. Singh and X. Vives, Price and quantity competition in a differentiated duopoly,, In, 15 (1984), 546.   Google Scholar

show all references

References:
[1]

C. d'Aspremont and A. Jacquemin, Cooperative and noncooperative R$&$D in duopoly with spillovers,, In, 78 (1988), 1133.   Google Scholar

[2]

J. A. Brander and B. J. Spencer, Strategic commitment with R$&$D: The symmetric case,, In, 14 (1983), 225.   Google Scholar

[3]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses,, Paris, (1838).   Google Scholar

[4]

F. A. Ferreira, F. Ferreira, M. Ferreira and A. A. Pinto, "Quantity Competition in a Differentiated Duopoly. Intelligent Engineering Systems and Computational Cybernetics,", Springer Netherlands, (2008).   Google Scholar

[5]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Patents in new technologies,, In, 15 (2009), 1135.   Google Scholar

[6]

M. Ferreira, I. F. Figueiredo, B. M. P. M. Oliveira and A. A. Pinto, Strategic optimization in R&D Investment,, In, (2011).   Google Scholar

[7]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Piecewise R&D Dynamics on costs,, In, 44 (2010), 29.   Google Scholar

[8]

A. A. Pinto, B. Oliveira, F. A. Ferreira and M. Ferreira, "Investing to Survive in a Duopoly Model. Intelligent Engineering Systems and Computational Cybernetics,", Springer Netherlands, (2008).   Google Scholar

[9]

L. Ruff,., Research and technological progress in a Cournot economy,, In, 1 (1969), 397.   Google Scholar

[10]

J. Tirole, "The Theory of Industrial Organization,", MIT Press, (1988).   Google Scholar

[11]

N. Singh and X. Vives, Price and quantity competition in a differentiated duopoly,, In, 15 (1984), 546.   Google Scholar

[1]

Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347

[2]

Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020051

[3]

Xuhui Peng, Rangrang Zhang. Approximations of stochastic 3D tamed Navier-Stokes equations. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5337-5365. doi: 10.3934/cpaa.2020241

[4]

Xin-Guang Yang, Lu Li, Xingjie Yan, Ling Ding. The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay. Electronic Research Archive, 2020, 28 (4) : 1395-1418. doi: 10.3934/era.2020074

[5]

Justin Holmer, Chang Liu. Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020264

[6]

Wenmeng Geng, Kai Tao. Large deviation theorems for dirichlet determinants of analytic quasi-periodic jacobi operators with Brjuno-Rüssmann frequency. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5305-5335. doi: 10.3934/cpaa.2020240

[7]

Denis Bonheure, Silvia Cingolani, Simone Secchi. Concentration phenomena for the Schrödinger-Poisson system in $ \mathbb{R}^2 $. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020447

[8]

Mathew Gluck. Classification of solutions to a system of $ n^{\rm th} $ order equations on $ \mathbb R^n $. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5413-5436. doi: 10.3934/cpaa.2020246

[9]

Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $. Electronic Research Archive, , () : -. doi: 10.3934/era.2020123

[10]

Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457

[11]

Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020464

[12]

Lei Liu, Li Wu. Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020378

[13]

Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

[14]

Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

[15]

Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219

[16]

Zhouchao Wei, Wei Zhang, Irene Moroz, Nikolay V. Kuznetsov. Codimension one and two bifurcations in Cattaneo-Christov heat flux model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020344

[17]

Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020349

[18]

Barbora Benešová, Miroslav Frost, Lukáš Kadeřávek, Tomáš Roubíček, Petr Sedlák. An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020459

[19]

Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

[20]

Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020431

 Impact Factor: 

Metrics

  • PDF downloads (19)
  • HTML views (0)
  • Cited by (0)

[Back to Top]