American Institute of Mathematical Sciences

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

R&d dynamics

J. Becker 1, , M. Ferreira 2, , B.M.P.M. Oliveira 2, and  A.A. Pinto 1,

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.
Keywords: Nash $R\&D$ investment strategies, duopoly model..
Mathematics Subject Classification: 91A10, 91A4.
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 "American Economic Review," 78 (1988), 1133-1137, (Erratum. In " American Economic Review," 80 641-642. Google Scholar

[2]

J. A. Brander and B. J. Spencer, Strategic commitment with R$&$D: The symmetric case, In "The Bell Journal of Economics," 14 (1983), 225-235. Google Scholar

[3]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Paris, 1838. English edition: Researches into the Mathematical Principles of the Theory of Wealth. Edited by N. Bacon. New York: Macmillan, 1897. 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, Chapter 30, 2008.  Google Scholar

[5]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Patents in new technologies, In "Journal of Difference equations and Applications," 15 (2009), 1135-1149.  Google Scholar

[6]

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

[7]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Piecewise R&D Dynamics on costs, In " Fasciculi Mathematici," 44 (2010), 29-42.  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, Chapter 23, 2008. Google Scholar

[9]

L. Ruff,., Research and technological progress in a Cournot economy, In "Journal of Economic Theory," 1 (1969), 397-415.  Google Scholar

[10]

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

[11]

N. Singh and X. Vives, Price and quantity competition in a differentiated duopoly, In "RAND Journal of Economics," 15 (1984), 546-554. Google Scholar

show all references

References:
[1]

C. d'Aspremont and A. Jacquemin, Cooperative and noncooperative R$&$D in duopoly with spillovers, In "American Economic Review," 78 (1988), 1133-1137, (Erratum. In " American Economic Review," 80 641-642. Google Scholar

[2]

J. A. Brander and B. J. Spencer, Strategic commitment with R$&$D: The symmetric case, In "The Bell Journal of Economics," 14 (1983), 225-235. Google Scholar

[3]

A. Cournot, Recherches sur les Principes Mathématiques de la Théorie des Richesses, Paris, 1838. English edition: Researches into the Mathematical Principles of the Theory of Wealth. Edited by N. Bacon. New York: Macmillan, 1897. 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, Chapter 30, 2008.  Google Scholar

[5]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Patents in new technologies, In "Journal of Difference equations and Applications," 15 (2009), 1135-1149.  Google Scholar

[6]

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

[7]

M. Ferreira, B. M. P. M. Oliveira and A. A. Pinto, Piecewise R&D Dynamics on costs, In " Fasciculi Mathematici," 44 (2010), 29-42.  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, Chapter 23, 2008. Google Scholar

[9]

L. Ruff,., Research and technological progress in a Cournot economy, In "Journal of Economic Theory," 1 (1969), 397-415.  Google Scholar

[10]

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

[11]

N. Singh and X. Vives, Price and quantity competition in a differentiated duopoly, In "RAND Journal of Economics," 15 (1984), 546-554. Google Scholar

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