Skip to main content
SpringerLink
Log in

R&D Dynamics with Asymmetric Efficiency

  • Conference paper
  • First Online:
Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2012)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 180))

Included in the following conference series:

Abstract

We consider an R&D investment function in a Cournot duopoly competition model inspired in the logistic equation. We study the economical effects resulting from the firms having different R&D efficiencies. We present three cases: (1) both firms are efficient and have the same degree of efficiency; (2) both firms are less efficient and have the same degree of efficiency; (3) firms are asymmetric in terms of the efficiency of their R&D investment programs. We study the myopic dynamics on the production costs obtained from investing the Nash investment equilibria.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Brander, J.A., Spencer, B.J.: Strategic commitment with R&D: the symmetric case. Bell J. Econ. 14, 225–235 (1983)

    Google Scholar 

  2. Cournot, A.: 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 

  3. d’Aspremont, C., Jacquemin, A.: Cooperative and noncooperative R and D in duopoly with spillovers. In: American Economic Review, vol. 78, pp. 1133–1137 (1988). (Erratum. 80, 641–642)

    Google Scholar 

  4. DeBondt, R.: Spillovers and innovative activities. Int. J. Industr. Organ. 15, 1–28 (1997)

    Article  Google Scholar 

  5. Ferreira, M., Oliveira, B.M.P.M., Pinto, A.A.: Patents in new technologies. J. Diff. Equ. Appl. 15, 1135–1149 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ferreira, M., Oliveira, B.M.P.M., Pinto, A.A.: Piecewise R and D dynamics on costs. Fasciculi Mathematici 44, 1–13 (2010)

    MathSciNet  MATH  Google Scholar 

  7. Kamien, M., Muller, E., Zang, I.: Research joint ventures and R and D cartels. Am. Econ. Rev. 82, 1293–1306 (1992)

    Google Scholar 

  8. Kamien, M., Zang, I.: Competing research joint ventures. J. Econ. Manag. Strateg. 2, 23–40 (1993)

    Article  Google Scholar 

  9. Katz, M.: An analysis of cooperative research and development. Rand J. Econ. 17, 527–543 (1986)

    Article  Google Scholar 

  10. Tirole, J.: The Theory of Industrial Organization. MIT Press, Massachusetts (1988)

    Google Scholar 

  11. Singh, N., Vives, X.: Price and quantity competition in a differentiated duopoly. RAND J. Econ. 15, 546–554 (1984)

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank LIAAD – INESC TEC and to acknowledge the financial support received by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation – COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961, and by National Funds through the FCT – Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2013 and by National Funds through the FCT within Project “Dynamics, optimization and modelling” with reference PTDC/MAT-NAN/6890/2014. Alberto Adrego Pinto also acknowledges the financial support received through the Special Visiting Researcher Program (Bolsa Pesquisador Visitante Especial – PVE) “Dynamics, Games and Applications” with reference 401068/2014-5 (call: MEC/MCTI/ CAPES/CNPQ/FAPS), at IMPA, Brazil. Bruno Oliveira gratefully acknowledges financial support from PRODEP III by FSE and EU and Miguel Ferreira gratefully acknowledges financial support from Fundação para a Ciência e a Tecnologia (FCT) given in the form of a PhD scholarship.

Author information

Authors and Affiliations

  1. LIAAD-INESC TEC and ESEIG-IPP, Rua D. Sancho I, 981, 4480-876, Vila Do Conde, Portugal

    M. Ferreira

  2. LIAAD-INESC TEC and Polytechnic Institute of Bragança, Campus de Santa Apolónia, 5300-253, Braganca, Portugal

    J. P. Almeida

  3. LIAAD-INESC TEC and FCNAUP, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    B. M. P. M. Oliveira

  4. LIAAD-INESC TEC and Department of Mathematics, FCUP, Rua Do Campo Alegre 687, 4169-007, Porto, Portugal

    Alberto A. Pinto

Authors
  1. M. Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. P. Almeida
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. M. P. M. Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alberto A. Pinto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. P. Almeida .

Editor information

Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, Barcelona, Spain

    Lluís Alsedà i Soler

  2. Department of Mathematics, University of Arizona, Tucson, Arizona, USA

    Jim M. Cushing

  3. Department of Mathematics, Trinity University, San Antonio, Texas, USA

    Saber Elaydi

  4. Faculty of Sciences, Department of Mathematics, University of Porto, Porto, Portugal

    Alberto A. Pinto

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ferreira, M., Almeida, J.P., Oliveira, B.M.P.M., Pinto, A.A. (2016). R&D Dynamics with Asymmetric Efficiency. In: Alsedà i Soler, L., Cushing, J., Elaydi, S., Pinto, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2012. Springer Proceedings in Mathematics & Statistics, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52927-0_6

Download citation

Publish with us

Policies and ethics

Search

Navigation