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Process and product innovation: A differential game approach to product life cycle

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  • Luca Lambertini
  • Andrea Mantovani

Abstract

We investigate the timing of adoption of product and process innovation using a differential game where firms may invest in both activities. We consider horizontal product innovation that reduces product substitutability, and process innovation that reduces marginal cost. First, we demonstrate that the incentive for cost‐reducing investment is relatively higher than the incentive to increase product differentiation. Second, depending on initial conditions: (i) firms activate both types of investment from the very outset to the steady state; (ii) firms initially invest in only one R&D activity and then reach the steady state either carrying out only this activity or carrying out both; or (iii) firms do not invest at all in either type of innovation. Comparing R&D investments under Cournot and Bertrand behavior shows that quantity competition entails lower R&D incentives than price competition in both directions.

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  • Luca Lambertini & Andrea Mantovani, 2010. "Process and product innovation: A differential game approach to product life cycle," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(2), pages 227-252, June.
  • Handle: RePEc:bla:ijethy:v:6:y:2010:i:2:p:227-252
    DOI: 10.1111/j.1742-7363.2010.00132.x
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    2. Bondarev, Anton, 2014. "Endogenous specialization of heterogeneous innovative activities of firms under the technological spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 235-249.
    3. Basak, Debasmita & Mukherjee, Arijit, 2018. "Labour unionisation structure and product innovation," International Review of Economics & Finance, Elsevier, vol. 55(C), pages 98-110.
    4. Bondarev, Anton & Greiner, Alfred, 2018. "Catching-up and falling behind: Effects of learning in an R&D differential game with spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 134-156.
    5. Bondarev, Anton A., 2012. "Optimal control over a continuous range of homogeneous and heterogeneous innovations with finite life-cycles," MPRA Paper 40068, University Library of Munich, Germany.
    6. Luca Lambertini & Raimondello Orsini, 2015. "Quality Improvement and Process Innovation in Monopoly: A Dynamic Analysis," Working Paper series 15-12, Rimini Centre for Economic Analysis.
    7. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2016. "R&D Cooperatives and Market Collusion: A Global Dynamic Approach," Tinbergen Institute Discussion Papers 16-048/II, Tinbergen Institute.
    8. Hinloopen, Jeroen & Smrkolj, Grega & Wagener, Florian, 2013. "In Defense of Trusts: R&D Cooperation in Global Perspective," MPRA Paper 63551, University Library of Munich, Germany, revised 09 Apr 2015.
    9. Bondarev, Anton, 2018. "Does stronger intellectual property rights protection foster structural change? Effects of heterogeneity in innovations," Structural Change and Economic Dynamics, Elsevier, vol. 46(C), pages 26-42.
    10. Eckel, Carsten & Unger, Florian, 2015. "Credit constraints, endogenous innovations, and price setting in international trade," Discussion Papers in Economics 24858, University of Munich, Department of Economics.
    11. Jason M. Walter & Jeffrey M. Peterson, 2017. "Strategic R&D and the innovation of products: understanding the role of time preferences and product differentiation," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 26(7), pages 575-595, October.
    12. Debasmita Basak & Andreas Hoefele & Arijit Mukherjee, 2014. "Union Bargaining Power and Product Innovation: Relevance of the Preference Function," CESifo Working Paper Series 5007, CESifo.
    13. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2017. "Research and Development Cooperatives and Market Collusion: A Global Dynamic Approach," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 567-612, August.
    14. L. Lambertini & R. Orsini, 2014. "Process Innovation and Product Quality Improvement in a Dynamic Monopoly," Working Papers wp926, Dipartimento Scienze Economiche, Universita' di Bologna.
    15. Lambertini, Luca & Orsini, Raimondello & Palestini, Arsen, 2017. "On the instability of the R&D portfolio in a dynamic monopoly. Or, one cannot get two eggs in one basket," International Journal of Production Economics, Elsevier, vol. 193(C), pages 703-712.
    16. Ni, Jian & Zhao, Jun & Chu, Lap Keung, 2021. "Supply contracting and process innovation in a dynamic supply chain with information asymmetry," European Journal of Operational Research, Elsevier, vol. 288(2), pages 552-562.
    17. Anton Bondarev, 2016. "Intensity of R&D competition and the generation of innovations in heterogeneous setting," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 621-653, July.
    18. Li, Shoude & Ni, Jian, 2016. "A dynamic analysis of investment in process and product innovation with learning-by-doing," Economics Letters, Elsevier, vol. 145(C), pages 104-108.
    19. Colin Davis & Yasunobu Tomoda, 2018. "Competing incremental and breakthrough innovation in a model of product evolution," Journal of Economics, Springer, vol. 123(3), pages 225-247, April.
    20. Debasmita Basak & Arijit Mukherjee, 2011. "Unionisation structure and product innovation," Discussion Papers 11/12, University of Nottingham, School of Economics.

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