\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Cooperative and noncooperative R&D in duopoly manufacturers with a common supplier

  • *Corresponding author: Yangyang Peng

    *Corresponding author: Yangyang Peng 
Abstract / Introduction Full Text(HTML) Figure(4) / Table(4) Related Papers Cited by
  • We consider the R&D strategy of firms under competitive environments from the supply chain perspective. Specifically, we investigate a supply chain consisting of one upstream component supplier and two downstream manufacturers, who however are the Stackelberg leader(s). At the early stage (R&D stage), the two manufacturers decide on whether to cooperate or not in the R&D activities and how much to invest in R&D accordingly. At the late stage (market stage), the component supplier decides on the uniform wholesale price and the manufacturers decide on the production quantities. Our main findings include: (ⅰ) Cooperative R&D strategy will be adopted when the technology spillover effect is either too large or too small and in contrast non-cooperative strategy will be accepted when the spillover effect is moderate. However, the underlying driving forces for coordination are different when the spillover effect is small or large, i.e., cost reduction effect and sales increasing effect. (ⅱ) Cooperative R&D could increase the social welfare when both the technology spillover effect and the (initial) unit production cost are high. (ⅲ) As the equilibrium under the cooperative R&D strategy is unstable, we give a coordination mechanism, to guarantee the stability of cooperative R&D investments.

    Mathematics Subject Classification: Primary: 90B06, 90B50; Secondary: 91A80.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  The Four-Stage Game between Upstream Supplier and Downstream Manufacturers

    Figure 2.  Optimal R&D Strategies for Downstream Manufacturers

    Figure 3.  The R&D Decision Matrix

    Figure 4.  The Effect of Supplier's Willingness to Cooperate

    Table 1.  The Equilibrium Outcomes in Noncooperative R&D Strategy

    Scenario $ c_n(\beta)<c_d<a-c_u $ $ 0<c_d \le c_n(\beta) $
    $ x_i^N $ $ \frac{{(7 - 5\beta )k}}{{29 - 2\beta + 5{\beta ^2}}} $ $ \frac{{{c_d}}}{{1 + \beta }} $
    $ w^N $ $ \frac{{18(a - {c_d}) + (11 - 2\beta + 5{\beta ^2}){c_u}}}{{29 - 2\beta + 5{\beta ^2}}} $ $ \frac{{a + {c_u}}}{2} $
    $ p^N $ $ \frac{{a(17 - 2\beta + 5{\beta ^2}) + 12({c_u} + {c_d})}}{{29 - 2\beta + 5{\beta ^2}}} $ $ \frac{{2a + {c_u}}}{3} $
    $ q_i^N $ $ \frac{{6k}}{{29 - 2\beta + 5{\beta ^2}}} $ $ \frac{{a - {c_u}}}{6} $
    $ \pi_u^N $ $ \frac{{216{k^2}}}{{{{(29 - 2\beta + 5{\beta ^2})}^2}}} $ $ \frac{{{{(a - {c_u})}^2}}}{6} $
    $ \pi_i^N $ $ \frac{{(23 + 70\beta - 25{\beta ^2}){k^2}}}{{2{{(29 - 2\beta + 5{\beta ^2})}^2}}} $ $ \frac{{{{(a - {c_u})}^2}{{(1 + \beta )}^2} - 18c_d^2}}{{36{{(1 + \beta )}^2}}} $
     | Show Table
    DownLoad: CSV

    Table 2.  The Equilibrium Outcomes in Cooperative R&D Strategy

    Scenario $ c_o(\beta)<c_d<a-c_u $ $ 0<c_d \le c_o(\beta) $
    $ x_i^C $ $ \frac{{k(1 + \beta )}}{{17 - 2\beta - {\beta ^2}}} $ $ \frac{{{c_d}}}{{1 + \beta }} $
    $ w^C $ $ \frac{{9(a - {c_d}) + (8 - 2\beta - {\beta ^2}){c_u}}}{{17 - 2\beta - {\beta ^2}}} $ $ \frac{{a + {c_u}}}{2} $
    $ p^C $ $ \frac{{a(11 - 2\beta - {\beta ^2}) + 6({c_u} + {c_d})}}{{17 - 2\beta - {\beta ^2}}} $ $ \frac{{2a + {c_u}}}{3} $
    $ q_i^C $ $ \frac{{3k}}{{17 - 2\beta - {\beta ^2}}} $ $ \frac{{a - {c_u}}}{6} $
    $ \pi_u^C $ $ \frac{{54{k^2}}}{{{{(17 - 2\beta - {\beta ^2})}^2}}} $ $ \frac{{{{(a - {c_u})}^2}}}{6} $
    $ \pi_i^C $ $ \frac{{{k^2}}}{{2(17 - 2\beta - {\beta ^2})}} $ $ \frac{{{{(a - {c_u})}^2}{{(1 + \beta )}^2} - 18c_d^2}}{{36{{(1 + \beta )}^2}}} $
     | Show Table
    DownLoad: CSV

    Table 3.  The Equilibrium Outcomes in Cooperative R&D Strategy

    Scenario $ c_o(\beta)<c_d<a-c_u $ $ 0<c_d \le c_o(\beta) $
    $ x_i^C $ $ \frac{{k(1 + \beta(1+\theta) )}}{{17 - 2\beta(1+\theta) - {(\beta(1+\theta)) ^2}}} $ $ \frac{{{c_d}}}{{1 + \beta(1+\theta) }} $
    $ w^C $ $ \frac{{9(a - {c_d}) + (8 - 2\beta(1+\theta) - {(\beta(1+\theta)) ^2}){c_u}}}{{17 - 2\beta(1+\theta) - {(\beta(1+\theta)) ^2}}} $ $ \frac{{a + {c_u}}}{2} $
    $ p^C $ $ \frac{{a(11 - 2\beta(1+\theta) - {(\beta(1+\theta))^2}) + 6({c_u} + {c_d})}}{{17 - 2\beta(1+\theta) - {(\beta(1+\theta))^2}}} $ $ \frac{{2a + {c_u}}}{3} $
    $ q_i^C $ $ \frac{{3k}}{{17 - 2\beta(1+\theta) - {(\beta(1+\theta)) ^2}}} $ $ \frac{{a - {c_u}}}{6} $
    $ \pi_u^C $ $ \frac{{54{k^2}}}{{{{(17 - 2\beta(1+\theta) - {(\beta(1+\theta) )^2})}^2}}} $ $ \frac{{{{(a - {c_u})}^2}}}{6} $
    $ \pi_i^C $ $ \frac{{{k^2}}}{{2(17 - 2\beta(1+\theta) - {(\beta(1+\theta) )^2})}} $ $ \frac{{{{(a - {c_u})}^2}{{(1 + \beta(1+\theta) )}^2} - 18c_d^2}}{{36{{(1 + \beta(1+\theta) )}^2}}} $
     | Show Table
    DownLoad: CSV

    Table 4.  The Equilibrium Outcomes in Noncooperative R&D Strategy

    Scenario $ c_n(\beta)<c_d<a-c_u $ $ 0<c_d \le c_n(\beta) $
    $ x_i^N $ $ \frac{{(7 - 5\beta(1+\theta) )k}}{{29 - 2\beta(1+\theta) + 5{(\beta(1+\theta) )^2}}} $ $ \frac{{{c_d}}}{{1 + \beta(1+\theta) }} $
    $ w^N $ $ \frac{{18(a - {c_d}) + (11 - 2\beta(1+\theta) + 5{(\beta(1+\theta) )^2}){c_u}}}{{29 - 2\beta(1+\theta) + 5{(\beta(1+\theta) )^2}}} $ $ \frac{{a + {c_u}}}{2} $
    $ p^N $ $ \frac{{a(17 - 2\beta(1+\theta) + 5{(\beta(1+\theta)) ^2}) + 12({c_u} + {c_d})}}{{29 - 2\beta(1+\theta) + 5{(\beta(1+\theta)) ^2}}} $ $ \frac{{2a + {c_u}}}{3} $
    $ q_i^N $ $ \frac{{6k}}{{29 - 2\beta(1+\theta) + 5{(\beta(1+\theta))^2}}} $ $ \frac{{a - {c_u}}}{6} $
    $ \pi_u^N $ $ \frac{{216{k^2}}}{{{{(29 - 2\beta(1+\theta) + 5{(\beta(1+\theta))^2})}^2}}} $ $ \frac{{{{(a - {c_u})}^2}}}{6} $
    $ \pi_i^N $ $ \frac{{(23 + 70\beta(1+\theta) - 25{(\beta(1+\theta))^2}){k^2}}}{{2{{(29 - 2\beta(1+\theta) + 5{(\beta(1+\theta))^2})}^2}}} $ $ \frac{{{{(a - {c_u})}^2}{{(1 + \beta(1+\theta) )}^2} - 18c_d^2}}{{36{{(1 + \beta(1+\theta) )}^2}}} $
     | Show Table
    DownLoad: CSV
  • [1] R. Amir and J. Wooders, Cooperation vs. competition in R&D: The role of stability of equilibrium, Journal of Economics, 1 (1998), 63-73. 
    [2] R. Amir, Modelling imperfectly appropriable R&D via spillovers, International Journal of Industrial Organization, 7 (2000), 1013-1032. 
    [3] K. ArrowEconomic Welfare and the Allocation of Resources for Invention, Princeton University Press, Princeton, NJ, 1962. 
    [4] G. Atallah, Vertical R&D spillovers, cooperation, market structure, and innovation, Economics of Innovation and New Technology, 3 (2002), 179-209. 
    [5] C. Atiyeh, BMW and Mercedes-Benz will stop fighting and join forces to make a better autonomous car, Car and Driver, https://www.caranddriver.com/news/a26572775/bmw-and-mercedes-benz-joint-autonomous-car/, (2019).
    [6] K. Brockhoff, R&D cooperation between firms-A perceived transaction cost perspective, Management Science, 4 (1992), 514-524. 
    [7] P. G. CanbolatB. GolanyI. Mund and U. G. Rothblum, A stochastic competitive R&D race where "winner takes all", Operations Research, 3 (2012), 700-715.  doi: 10.1287/opre.1120.1055.
    [8] R. Cellini and L. Lambertini, A differential game approach to investment in product differentiation, Journal of Economic Dynamics and Control, 1 (2002), 51-62.  doi: 10.1016/S0165-1889(01)00026-4.
    [9] R. Cellini and L. Lambertini, Dynamic R&D with spillovers: Competition vs cooperation, Journal of Economic Dynamics and Control, 33 (2009), 568-582.  doi: 10.1016/j.jedc.2008.08.006.
    [10] Chinadaily, Vivo and Samsung make a joint push into 5G smartphone chip, Chinadaily, https://www.chinadaily.com.cn/a/201911/08/WS5dc50472a310cf3e355763a3.html, (2019).
    [11] S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 4 (1991), 271-296. 
    [12] X. ChenX. Wang and M. Zhou, Firms' green R&D cooperation behaviour in a supply chain: Technological spillover, power and coordination, International Journal of Production Economics, 219 (2019), 118-134. 
    [13] C. PascaleB. De Reyck and N. Taneri, Licensing contracts: Control rights, options, and timing, Management Science, 4 (2017), 1131-1149. 
    [14] C. D'Aspremont and A. Jacquemin, Cooperative and noncooperative R&D in duopoly with spillovers, American Economic Review, 5 (1988), 1133-1137. 
    [15] M. Del GiudiceV. ScuottoA. Garcia-Perez and A. M. Petruzzelli, Shifting wealth II in Chinese economy. The effect of the horizontal technology spillover for SMEs for international growth, Technological Forecasting and Social Change, 145 (2019), 307-316.  doi: 10.1016/j.techfore.2018.03.013.
    [16] Ericsson, Ericsson and OPPO sign initial patent license agreement, Ericsson, https://www.ericsson.com/en/press-releases/2019/2/ericsson-and-oppo-sign-initial-patent-license-agreement, (2019).
    [17] N. Erkal and D. Piccinin, Cooperative R&D under uncertainty with free entry, International Journal of Industrial Organization, 1 (2010), 74-85. 
    [18] R. Falvey and K. T. Teerasuwannajak, Competitive and harmonized R&D policies for international R&D alliances involving asymmetric firms, Review of international economics, 2 (2016), 302-329. 
    [19] Z. GeQ. Hu and Y. Xia, Firms' R&D cooperation behavior in a supply chain, Production and Operations Management, 4 (2014), 599-609. 
    [20] I. Henriques, Cooperative and noncooperative R&D in duopoly with spillovers: Comment, American Economic Review, 3 (1990), 638-640. 
    [21] A. Ishii, Cooperative R&D between vertically related firms with spillovers, International Journal of Industrial Organization, 9 (2004), 1213-1235. 
    [22] N. Ishikawa and T. Shibata, Market competition, R&D spillovers, and firms' cost asymmetry, Economics of Innovation and New Technology, (2019), 1–19.
    [23] P. T. Joanna, Equilibrium and optimal size of a research joint venture in an oligopoly with spillovers, Journal of Industrial Economics, 2 (1995), 209-226. 
    [24] T. Kabiraj and S. Chattopadhyay, Cooperative vs. non-cooperative R&D incentives under incomplete information, Economics of Innovation and New Technology, 6 (2015), 624-632. 
    [25] M. I. KamienE. Muller and I. Zang, Research joint ventures and R&D cartels, American Economic Review, 5 (1992), 1293-1306. 
    [26] P. S. KohD. M. Reeb and W. Zhao, CEO confidence and unreported R&D, Management Science, 12 (2018), 5725-5747. 
    [27] J. L. Krieger, Trials and terminations: Learning from competitors' R&D failures, Management Science, first online, (2021).
    [28] S. Marjit, Incentives for cooperative and non-cooperative R&D in duopoly, Economics Letters, 2 (1991), 187-191. 
    [29] J. A. Martin and K. M. Eisenhardt, Rewiring: Cross-Business-Unit collaborations in multibusiness organizations, Academy of Management Journal, 2 (2010), 265-301. 
    [30] M. Motta, Cooperative R&D and vertical product differentiation, International Journal of Industrial Organization, 4 (1992), 643-661. 
    [31] J. Ning and V. Babich, R&D investments in the presence of knowledge spillover and debt financing: Can risk shifting cure free riding?, Manufacturing & Service Operations Management, 1 (2018), 97-112. 
    [32] C. PennetierK. Girotra and J. Mihm, R&D spending: Dynamic or persistent?, Manufacturing & Service Operations Management, 3 (2019), 636-657. 
    [33] G. Smrkolj and F. Wagener, Dynamic R&D with spillovers: A comment, Journal of Economic Dynamics and Control, 2 (2016), 453-457.  doi: 10.1016/j.jedc.2016.10.011.
    [34] M. Spence, Cost reduction, competition, and industry performance, Econometrica, 1 (1984), 101-121. 
    [35] L. Suzumura, Cooperative and noncooperative R&D in an oligopoly with spillovers, American Economic Review, 5 (1992), 1307-1320. 
    [36] Y. Taba, Optimal product R&D policies with endogenous quality choices and unilateral spillover, Journal of Economic Analysis & Policy, 1 (2016), 365-391. 
    [37] L. XuD. LiangZ. Duan and X. Xiao, Stability analysis of R&D cooperation in a supply chain, Mathematical Problems in Engineering, 8 (2015), 1-10.  doi: 10.1155/2015/409286.
    [38] M. Xing, The optimal risk choice of cooperative and noncooperative R&D in duopoly with spillovers, Bulletin of Economic Research, 4 (2017), 173-185.  doi: 10.1111/boer.12109.
    [39] D. ZengL. Xu and X. Bi, Effects of asymmetric knowledge spillovers on the stability of horizontal and vertical R&D cooperation, Computational and Mathematical Organization Theory, 1 (2017), 32-60. 
    [40] S. K. ByunJ. Min and H. Xia, Incremental vs. Breakthrough innovation: The role of technology spillovers, Management Science, 3 (2021), 1779-1802. 
    [41] N. BloomM. Schankerman and J. Van Reenen, Identifying technology spillovers and product market rivalry, Econometrica, 4 (2013), 1347-1393.  doi: 10.3982/ECTA9466.
    [42] J. Qiu and C. Wan, Technology spillovers and corporate cash holdings, Journal of Financial Economics, 3 (2015), 558-573. 
    [43] X. PanM. LiM. WangJ. Chu and H. Bo, The effects of outward foreign direct investment and reverse technology spillover on China's carbon productivity, Energy Policy, 145 (2020), 111730. 
    [44] Y. Hu, K. Fisher-Vanden and B. Su, Technological spillover through industrial and regional linkages: Firm-level evidence from China, Economic Modelling, 89 (2020).
    [45] Y. GaoS. B. TsaiX. XueT. RenX. DuQ. Chen and et al., An empirical study on green innovation efficiency in the green institutional environment, Sustainability, 3 (2018), 724. 
    [46] A. Ll, A. Zz, A. Mz, A. Cz and B. Dz, The effects of environmental regulation on outward foreign direct investment's reverse green technology spillover: Crowding out or facilitation?, Journal of Cleaner Production, 2 (2020).
    [47] Z. Cheng and B. R. Nault, Relative industry concentration and customer-driven it spillovers, Information Systems Research, 2 (2012), 340-355. 
    [48] P. Tambe and L. M. Hitt, Measuring information technology spillovers, Information Systems Research, 1 (2013), 53-71. 
    [49] P. Tambe and L. M. Hitt, Job hopping, information technology spillovers, and productivity growth, Management Science, 2 (2013), 338-355. 
    [50] X. QinD. Du and M. P. Kwan, Spatial spillovers and value chain spillovers: Evaluating regional R&D efficiency and its spillover effects in China, Scientometrics, 119 (2019), 721-747. 
    [51] N. Ishikawa and T. Shibata, R&D competition and cooperation with asymmetric spillovers in an oligopoly market, International Review of Economics & Finance, 72 (2020), 624-642.  doi: 10.1016/j.iref.2020.12.016.
    [52] J. NiH. HuangP. Wang and W. Zhou, Capacity investment and green R&D in a dynamic oligopoly under the potential shift in environmental damage, Economic Modelling, 7 (2019), 312-319. 
    [53] C. LiP. Zhou and Y. Li, Managerial overconfidence, overinvestment, and R&D spillover, Managerial and Decision Economics, 40 (2019), 1-4. 
    [54] D. Zhang, H. Dai, L. Dong, F. Qi, N. Zhang, X. Liu, et al., The long-term and spillover effects of price promotions on retailing platforms: Evidence from a large randomized experiment on Alibaba, Management Science, 6 (2020), 2589–2609. doi: 10.1109/TSP.2021.3083988.
    [55] D. Y. Joe and F. D. Oh, Spillover effects within business groups: The case of Korean chaebols, Management Science, 3 (2018), 1396-1412. 
    [56] A. HavivY. Huang and N. Li, Intertemporal demand spillover effects on video game platforms, Management Science, 10 (2020), 4788-4807. 
  • 加载中

Figures(4)

Tables(4)

SHARE

Article Metrics

HTML views(2004) PDF downloads(406) Cited by(0)

Access History

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return