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Stochastic control model for R&D race in a mixed duopoly with spillovers and knowledge stocks

Listed author(s):
  • Jingjing Wang
  • Chi Leung
  • Yue Kwok

    ()

Registered author(s):

    We consider the stochastic control model with finite time horizon for a mixed duopoly Research and Development (R&D) race between the profit-maximizing private firm and welfare-maximizing public firm. In our two-firm stochastic control R&D race model with input and output spillovers, the stochastic control variable is taken to be the private firm’s rate of R&D expenditure and the hazard rate of success of innovation has dependence on the R&D effort and knowledge stock. Given the fixed R&D effort of the public firm, the optimal control is determined so as to maximize the private firm’s value function subject to market uncertainty arising from the stochastic profit flow of the new innovative product. We conduct various sensitivity tests with varying model parameters to analyze the effects of input spillover, output spillover and knowledge stock on the optimal control policy and the value function of the profit-maximizing private firm. The R&D effort of the private firm is found to increase when the profit flow rate increases. Moreover, the optimal R&D effort level may decrease with increasing private firm’s knowledge stock and output spillover. The effects of input spillover on the optimal control policy and value function are seen to be relatively small. We examine the robustness of various observed phenomena of the two-firm R&D race with varying values of the fixed R&D effort of the public firm. With regard to public policy issue, we examine the level of the fixed public firm’s R&D effort so that social welfare is maximized. Copyright Springer-Verlag Italia 2015

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    File URL: http://hdl.handle.net/10.1007/s10203-015-0163-z
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    Article provided by Springer & Associazione per la Matematica in its journal Decisions in Economics and Finance.

    Volume (Year): 38 (2015)
    Issue (Month): 2 (October)
    Pages: 177-195

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    Handle: RePEc:spr:decfin:v:38:y:2015:i:2:p:177-195
    DOI: 10.1007/s10203-015-0163-z
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    1. Naseem, Anwar & Oehmke, James F., 2006. "Spillovers, Joint Ventures and Social Welfare in a Mixed Duopoly R&D Race," 2006 Annual meeting, July 23-26, Long Beach, CA 21351, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Poyago-Theotoky, Joanna, 1998. "R&D Competition in a Mixed Duopoly under Uncertainty and Easy Imitation," Journal of Comparative Economics, Elsevier, vol. 26(3), pages 415-428, September.
    3. König, Michael D. & Battiston, S. & Napoletano, M. & Schweitzer, F., 2011. "Recombinant knowledge and the evolution of innovation networks," Journal of Economic Behavior & Organization, Elsevier, vol. 79(3), pages 145-164, August.
    4. Maria José Gil-Moltó & Joanna Poyago-Theotoky & Vasileios Zikos, 2011. "R&D Subsidies, Spillovers, and Privatization in Mixed Markets," Southern Economic Journal, Southern Economic Association, vol. 78(1), pages 233-255, July.
    5. Delbono, Flavio & Denicolo, Vincenzo, 1993. "Regulating innovative activity : The role of a public firm," International Journal of Industrial Organization, Elsevier, vol. 11(1), pages 35-48, March.
    6. Marco Marinucci, 2014. "Cooperative R&D networks among firms and public research institutions," Temi di discussione (Economic working papers) 962, Bank of Italy, Economic Research and International Relations Area.
    7. Vasileios Zikos, 2007. "Equilibrium and Optimal R&D Roles in a Mixed Market," Discussion Paper Series 2007_08, Department of Economics, Loughborough University, revised Mar 2007.
    8. Grzegorz Pawlina & Peter M. Kort, 2006. "Real Options in an Asymmetric Duopoly: Who Benefits from Your Competitive Disadvantage?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(1), pages 1-35, 03.
    9. de Fraja, Giovanni & Delbono, Flavio, 1990. " Game Theoretic Models of Mixed Oligopoly," Journal of Economic Surveys, Wiley Blackwell, vol. 4(1), pages 1-17.
    10. Steinmetz, Alexander, 2010. "Competition, innovation, and the effect of knowledge accumulation," W.E.P. - Würzburg Economic Papers 81, University of Würzburg, Chair for Monetary Policy and International Economics.
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