# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022023
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## Imitative innovation or independent innovation strategic choice of emerging economies in non-cooperative innovation competition

 School of Management, University of Science and Technology of China, Hefei, Anhui, China

*Corresponding author: Zhiying Liu

Received  April 2021 Revised  November 2021 Early access February 2022

The importance of knowledge and technology is self-evident, especially the core technology of key nodes in the industrial chain, which will change the country's status in the supply chain, and even the national economic security. This scenario has led to a global non-cooperative innovation competition. In order to ensure the safety of local industrial chain and shorten the technological distance with developed countries, emerging economies can adopt imitative innovation by observing the core technologies from developed countries, or choose independent innovation strategy. How should emerging economies make the choice? We analyze this problem by establishing a dynamic non-cooperative technology development model. The research results show that when the innovation capacity gap between emerging economies and developed regions is large, the choice of imitation strategy is highly necessary. And when the gap is small, the independent innovation strategy can be selected. In addition, due to the existence of both domestic and foreign markets, developed countries can adopt strict policies to restrict the sale of products containing core technologies to overseas markets to limit the spillover of important technologies. We also consider the impact of policies that limit technology spillovers and show the impact of local market capacity in emerging economies.

Citation: Yang Liu, Zhiying Liu, Kaifei Xu. Imitative innovation or independent innovation strategic choice of emerging economies in non-cooperative innovation competition. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022023
##### References:
 [1] C. D 'Aspremont and A. J. L. R. C. Jacquemin, Cooperative and Noncooperative R&D in Duopoly with Spillovers, LIDAM Reprints CORE, University catholique de Louvain, 1988. [2] G. Barboza and A. Capocchi, Innovative startups in Italy. Managerial challenges of knowledge spillovers effects on employment generation, Journal of Knowledge Management, 24 (2020), 2573-2596.  doi: 10.1108/JKM-08-2019-0436. [3] H. Ben Hassine, F. Boudier and C. Mathieu, He two ways of FDI R&D spillovers: Evidence from the French manufacturing industry, Applied Economics, 49 (2017), 2395-2408. [4] N. Bloom, M. Schankerman and J. Van Reenen, Identifying technology spillovers and product market rivalry, Econometrica, 81 (2013), 1347-1393.  doi: 10.3982/ECTA9466. [5] P. Boeing, The allocation and effectiveness of China's R&D subsidies - Evidence from listed firms, Research Policy, 45 (2016), 1774-1789. [6] A. Bondarev and A. Greiner, Catching-up and falling behind: Effects of learning in an R&D differential game with spillovers, J. Econom. Dynam. Control, 91 (2018), 134-156.  doi: 10.1016/j.jedc.2017.10.001. [7] J. W. B. Bos, C. Economidou and M. W. J. L. Sanders, Innovation over the industry life-cycle: Evidence from EU manufacturing, Journal of Economic Behavior & Organization, 86 (2013), 78-91.  doi: 10.1016/j.jebo.2012.12.025. [8] L. Branstetter, Vertical keiretsu and knowledge spillovers in Japanese manufacturing: An empirical assessment, Journal of the Japanese and International Economies, 14 (2000), 73-104.  doi: 10.1006/jjie.2000.0444. [9] S. Brianzoni, L. Gori and E. Michetti, Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences, Chaos Solitons Fractals, 79 (2015), 191-203.  doi: 10.1016/j.chaos.2015.05.014. [10] R. Cellini and L. Lambertini, A differential game approach to investment in product differentiation, J. Econom. Dynam. Control, 27 (2002), 51-62.  doi: 10.1016/S0165-1889(01)00026-4. [11] A. Doha, M. Pagell, M. Swink and D. Johnston, The imitator's dilemma: Why imitators should break out of imitation, Journal of Product Innovation Management, 35 (2018), 543-564. [12] A. A. Elsadany, Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization, Appl. Math. Comput., 294 (2017), 253-263.  doi: 10.1016/j.amc.2016.09.018. [13] N. Fabra and A. Garcia, Dynamic price competition with switching costs, Dyn. Games Appl., 5 (2015), 540-567.  doi: 10.1007/s13235-015-0157-z. [14] B. Feng, K. Sun, M. Chen and T. Gao, The impact of core technological capabilities of high-tech industry on sustainable competitive advantage, Sustainability, 12 (2020).  doi: 10.3390/su12072980. [15] D. Guo, Y. Guo and K. Jiang, Government-subsidized R&D and firm innovation: Evidence from china, Research Policy, 45 (2016), 1129-1144.  doi: 10.1016/j.respol.2016.03.002. [16] Gu pta and S. J. M. Sudheer, Research note-channel structure with knowledge spillovers, Marketing Science, 27 (2008), 247-261.  doi: 10.1287/mksc.1070.0285. [17] J. M. J. E. L. Hartwick, Optimal R&D levels when firm j benefits from firm i's inventive activity, Economics Letters, 16 (1984), 165-170.  doi: 10.1016/0165-1765(84)90158-7. [18] T. Haruyama and K.-i. Hashimoto, Innovators and imitators in a world economy, Journal of Economics, 130 (2020), 157-186.  doi: 10.1007/s00712-019-00688-2. [19] R. Henderson, Underinvestment and incompetence as responses to radical innovation: Evidence from the photolithographic alignment equipment industry, Rand Journal of Economics, 24 (1993), 248-270. [20] R. Henderson and I. Cockburn, Scale, scope, and spillovers: The determinants of research productivity in drug discovery, The Rand Journal of Economics, 27 (1996), 32-59. [21] J. Hinloopen, G. Smrkolj and F. Wagener, Research and development cooperatives and market collusion: A global dynamic approach, J. Optim. Theory Appl., 174 (2017), 567-612.  doi: 10.1007/s10957-017-1133-0. [22] A. J. N. B. o. E. R. Jaffe, Technological Opportunity and Spillovers of R&D: Evidence from Firms'Patents, Profits and Market Value, American Economic Review, Pittsburgh, 1986. doi: 10.3386/w1815. [23] K. L. Judd, Closed-loop equilibrium in a multi-stage innovation race, Econom. Theory, 21 (2003), 673-695.  doi: 10.1007/s00199-002-0310-y. [24] M. C. Kemp, N. V. Long and C. J. E. M. Chiarella, Innovation and the transfer of technology : A leader-follower model, Economic Modelling, 6 (1989), 452-456.  doi: 10.1016/0264-9993(89)90021-7. [25] L. Lambertini, The monopolist's optimal R&D portfolio, Oxford Economic Papers-New Series, 55 (2003), 561-578. [26] L. Lambertini and A. Mantovani, Process and product innovation: A differential game approach to product life cycle, International Journal of Economic Theory, 6 (2010), 227-252.  doi: 10.1111/j.1742-7363.2010.00132.x. [27] L. Lambertini and R. Orsini, Network externalities and the overprovision of quality by a monopolist, Southern Economic Journal, 67 (2001), 969-982.  doi: 10.1002/j.2325-8012.2001.tb00384.x. [28] L. J. R. o. E. A. Lambertini, Optimal product proliferation in monopoly: A dynamic analysis, Review of Economic Analysis, 1 (2009), 80-97.  doi: 10.15353/rea.v1i1.1480. [29] L. J. J. o. T. T. Lanahan, Multilevel public funding for small business innovation: A review of US state SBIR match programs, Journal of Technology Transfer, 41 (2016), 220-249.  doi: 10.1007/s10961-015-9407-x. [30] M. B. Lieberman, S. Asaba, W. Thank, J. Baum and L. Zucker, Why do firms imitate each other?, Academy of Management Review, 31 (2004).  doi: 10.5465/amr.2006.20208686. [31] S. Luckraz, R&D games in a Cournot duopoly with isoelastic demand functions: A comment, Economic Modelling, 28 (2011), 2873-2876.  doi: 10.1016/j.econmod.2011.07.019. [32] R. R. Nelson and G. J. j. o. E. L. Wright, The rise and fall of American technological leadership: The postwar era in historical perspective, Journal of Economic Literature, 30 (1992), 1931-1964. [33] X. Pan and S. Li, Dynamic optimal control of process-product innovation with learning by doing, European J. Oper. Res., 248 (2016), 136-145.  doi: 10.1016/j.ejor.2015.07.007. [34] B. A. Pansera, L. Guerrini, M. Ferrara and T. Ciano, Bifurcation analysis of a duopoly game with R&D spillover, price competition and time delays, Symmetry-Basel, 12 (2020).  doi: 10.3390/sym12020257. [35] P. V. Reddy and J. C. Engwerda, Necessary and sufficient conditions for pareto optimality in infinite horizon cooperative differential games, IEEE Trans. Automat. Control, 59 (2014), 2536-2542.  doi: 10.1109/TAC.2014.2305933. [36] P. V. Reddy and G. Zaccour, Open-loop nash equilibria in a class of linear-quadratic difference games with constraints, IEEE Trans. Automat. Control, 60 (2015), 2559-2564.  doi: 10.1109/TAC.2015.2394873. [37] J. F. Reinganum, A dynamic game of R-and-D - patent protection and competitive behavior, Econometrica, 50 (1982), 671-688.  doi: 10.2307/1912607. [38] H. Sakai, Depreciation rate of R&D capital: Panel data analysis of listed firms in japanese R&D-intensive industries contribution/ originality, Asian Economic and Financial Review, 6 (2016), 196-205.  doi: 10.18488/journal.aefr/2016.6.4/102.4.196.205. [39] Seierstad and K. J. N.-H. Sydsaeter, Optimal Control Theory with Economic Applications, Advanced Textbooks in Economics, 24. North-Holland Publishing Co., Amsterdam, 1987. [40] V. Shankar, G. Carpenter and L. Krishnamurthi, Late mover advantage, Journal of Marketing Research, 35 (1998), 54-70.  doi: 10.1177/002224379803500107. [41] G. Smrkolj and F. Wagener, Research among copycats: R&D, spillovers, and feedback strategies, International Journal of Industrial Organization, 65 (2019), 82-120.  doi: 10.1016/j.ijindorg.2019.02.002. [42] D. J. J. R. P. Teece, Profiting from technological innovation: Implications for integration, collaboration, licensing and public policy, Research Policy, 15 (1986). [43] Y. J. Yap, S. Luckraz and S. K. Tey, Long-term research and development incentives in a dynamic Cournot duopoly, Economic Modelling, 39 (2014), 8-18.  doi: 10.1016/j.econmod.2014.02.020. [44] W. Zhou, R.-R. Liu and T. Chu, Bifurcation global dynamics and synchronization in a Bertrand game with R&D spillover and semi-collusion, J. Difference Equ. Appl., 26 (2020), 1321-1346.  doi: 10.1080/10236198.2020.1831482. [45] W. Zhou and X.-X. Wang, On the stability and multistability in a duopoly game with R&D spillover and price competition, Discrete Dyn. Nat. Soc., 2019 (2019), Art. ID 2369898, 20 pp. doi: 10.1155/2019/2369898.

show all references

##### References:
 [1] C. D 'Aspremont and A. J. L. R. C. Jacquemin, Cooperative and Noncooperative R&D in Duopoly with Spillovers, LIDAM Reprints CORE, University catholique de Louvain, 1988. [2] G. Barboza and A. Capocchi, Innovative startups in Italy. Managerial challenges of knowledge spillovers effects on employment generation, Journal of Knowledge Management, 24 (2020), 2573-2596.  doi: 10.1108/JKM-08-2019-0436. [3] H. Ben Hassine, F. Boudier and C. Mathieu, He two ways of FDI R&D spillovers: Evidence from the French manufacturing industry, Applied Economics, 49 (2017), 2395-2408. [4] N. Bloom, M. Schankerman and J. Van Reenen, Identifying technology spillovers and product market rivalry, Econometrica, 81 (2013), 1347-1393.  doi: 10.3982/ECTA9466. [5] P. Boeing, The allocation and effectiveness of China's R&D subsidies - Evidence from listed firms, Research Policy, 45 (2016), 1774-1789. [6] A. Bondarev and A. Greiner, Catching-up and falling behind: Effects of learning in an R&D differential game with spillovers, J. Econom. Dynam. Control, 91 (2018), 134-156.  doi: 10.1016/j.jedc.2017.10.001. [7] J. W. B. Bos, C. Economidou and M. W. J. L. Sanders, Innovation over the industry life-cycle: Evidence from EU manufacturing, Journal of Economic Behavior & Organization, 86 (2013), 78-91.  doi: 10.1016/j.jebo.2012.12.025. [8] L. Branstetter, Vertical keiretsu and knowledge spillovers in Japanese manufacturing: An empirical assessment, Journal of the Japanese and International Economies, 14 (2000), 73-104.  doi: 10.1006/jjie.2000.0444. [9] S. Brianzoni, L. Gori and E. Michetti, Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences, Chaos Solitons Fractals, 79 (2015), 191-203.  doi: 10.1016/j.chaos.2015.05.014. [10] R. Cellini and L. Lambertini, A differential game approach to investment in product differentiation, J. Econom. Dynam. Control, 27 (2002), 51-62.  doi: 10.1016/S0165-1889(01)00026-4. [11] A. Doha, M. Pagell, M. Swink and D. Johnston, The imitator's dilemma: Why imitators should break out of imitation, Journal of Product Innovation Management, 35 (2018), 543-564. [12] A. A. Elsadany, Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization, Appl. Math. Comput., 294 (2017), 253-263.  doi: 10.1016/j.amc.2016.09.018. [13] N. Fabra and A. Garcia, Dynamic price competition with switching costs, Dyn. Games Appl., 5 (2015), 540-567.  doi: 10.1007/s13235-015-0157-z. [14] B. Feng, K. Sun, M. Chen and T. Gao, The impact of core technological capabilities of high-tech industry on sustainable competitive advantage, Sustainability, 12 (2020).  doi: 10.3390/su12072980. [15] D. Guo, Y. Guo and K. Jiang, Government-subsidized R&D and firm innovation: Evidence from china, Research Policy, 45 (2016), 1129-1144.  doi: 10.1016/j.respol.2016.03.002. [16] Gu pta and S. J. M. Sudheer, Research note-channel structure with knowledge spillovers, Marketing Science, 27 (2008), 247-261.  doi: 10.1287/mksc.1070.0285. [17] J. M. J. E. L. Hartwick, Optimal R&D levels when firm j benefits from firm i's inventive activity, Economics Letters, 16 (1984), 165-170.  doi: 10.1016/0165-1765(84)90158-7. [18] T. Haruyama and K.-i. Hashimoto, Innovators and imitators in a world economy, Journal of Economics, 130 (2020), 157-186.  doi: 10.1007/s00712-019-00688-2. [19] R. Henderson, Underinvestment and incompetence as responses to radical innovation: Evidence from the photolithographic alignment equipment industry, Rand Journal of Economics, 24 (1993), 248-270. [20] R. Henderson and I. Cockburn, Scale, scope, and spillovers: The determinants of research productivity in drug discovery, The Rand Journal of Economics, 27 (1996), 32-59. [21] J. Hinloopen, G. Smrkolj and F. Wagener, Research and development cooperatives and market collusion: A global dynamic approach, J. Optim. Theory Appl., 174 (2017), 567-612.  doi: 10.1007/s10957-017-1133-0. [22] A. J. N. B. o. E. R. Jaffe, Technological Opportunity and Spillovers of R&D: Evidence from Firms'Patents, Profits and Market Value, American Economic Review, Pittsburgh, 1986. doi: 10.3386/w1815. [23] K. L. Judd, Closed-loop equilibrium in a multi-stage innovation race, Econom. Theory, 21 (2003), 673-695.  doi: 10.1007/s00199-002-0310-y. [24] M. C. Kemp, N. V. Long and C. J. E. M. Chiarella, Innovation and the transfer of technology : A leader-follower model, Economic Modelling, 6 (1989), 452-456.  doi: 10.1016/0264-9993(89)90021-7. [25] L. Lambertini, The monopolist's optimal R&D portfolio, Oxford Economic Papers-New Series, 55 (2003), 561-578. [26] L. Lambertini and A. Mantovani, Process and product innovation: A differential game approach to product life cycle, International Journal of Economic Theory, 6 (2010), 227-252.  doi: 10.1111/j.1742-7363.2010.00132.x. [27] L. Lambertini and R. Orsini, Network externalities and the overprovision of quality by a monopolist, Southern Economic Journal, 67 (2001), 969-982.  doi: 10.1002/j.2325-8012.2001.tb00384.x. [28] L. J. R. o. E. A. Lambertini, Optimal product proliferation in monopoly: A dynamic analysis, Review of Economic Analysis, 1 (2009), 80-97.  doi: 10.15353/rea.v1i1.1480. [29] L. J. J. o. T. T. Lanahan, Multilevel public funding for small business innovation: A review of US state SBIR match programs, Journal of Technology Transfer, 41 (2016), 220-249.  doi: 10.1007/s10961-015-9407-x. [30] M. B. Lieberman, S. Asaba, W. Thank, J. Baum and L. Zucker, Why do firms imitate each other?, Academy of Management Review, 31 (2004).  doi: 10.5465/amr.2006.20208686. [31] S. Luckraz, R&D games in a Cournot duopoly with isoelastic demand functions: A comment, Economic Modelling, 28 (2011), 2873-2876.  doi: 10.1016/j.econmod.2011.07.019. [32] R. R. Nelson and G. J. j. o. E. L. Wright, The rise and fall of American technological leadership: The postwar era in historical perspective, Journal of Economic Literature, 30 (1992), 1931-1964. [33] X. Pan and S. Li, Dynamic optimal control of process-product innovation with learning by doing, European J. Oper. Res., 248 (2016), 136-145.  doi: 10.1016/j.ejor.2015.07.007. [34] B. A. Pansera, L. Guerrini, M. Ferrara and T. Ciano, Bifurcation analysis of a duopoly game with R&D spillover, price competition and time delays, Symmetry-Basel, 12 (2020).  doi: 10.3390/sym12020257. [35] P. V. Reddy and J. C. Engwerda, Necessary and sufficient conditions for pareto optimality in infinite horizon cooperative differential games, IEEE Trans. Automat. Control, 59 (2014), 2536-2542.  doi: 10.1109/TAC.2014.2305933. [36] P. V. Reddy and G. Zaccour, Open-loop nash equilibria in a class of linear-quadratic difference games with constraints, IEEE Trans. Automat. Control, 60 (2015), 2559-2564.  doi: 10.1109/TAC.2015.2394873. [37] J. F. Reinganum, A dynamic game of R-and-D - patent protection and competitive behavior, Econometrica, 50 (1982), 671-688.  doi: 10.2307/1912607. [38] H. Sakai, Depreciation rate of R&D capital: Panel data analysis of listed firms in japanese R&D-intensive industries contribution/ originality, Asian Economic and Financial Review, 6 (2016), 196-205.  doi: 10.18488/journal.aefr/2016.6.4/102.4.196.205. [39] Seierstad and K. J. N.-H. Sydsaeter, Optimal Control Theory with Economic Applications, Advanced Textbooks in Economics, 24. North-Holland Publishing Co., Amsterdam, 1987. [40] V. Shankar, G. Carpenter and L. Krishnamurthi, Late mover advantage, Journal of Marketing Research, 35 (1998), 54-70.  doi: 10.1177/002224379803500107. [41] G. Smrkolj and F. Wagener, Research among copycats: R&D, spillovers, and feedback strategies, International Journal of Industrial Organization, 65 (2019), 82-120.  doi: 10.1016/j.ijindorg.2019.02.002. [42] D. J. J. R. P. Teece, Profiting from technological innovation: Implications for integration, collaboration, licensing and public policy, Research Policy, 15 (1986). [43] Y. J. Yap, S. Luckraz and S. K. Tey, Long-term research and development incentives in a dynamic Cournot duopoly, Economic Modelling, 39 (2014), 8-18.  doi: 10.1016/j.econmod.2014.02.020. [44] W. Zhou, R.-R. Liu and T. Chu, Bifurcation global dynamics and synchronization in a Bertrand game with R&D spillover and semi-collusion, J. Difference Equ. Appl., 26 (2020), 1321-1346.  doi: 10.1080/10236198.2020.1831482. [45] W. Zhou and X.-X. Wang, On the stability and multistability in a duopoly game with R&D spillover and price competition, Discrete Dyn. Nat. Soc., 2019 (2019), Art. ID 2369898, 20 pp. doi: 10.1155/2019/2369898.
The differential field of the dynamical system before technology blockade
The differential field of the dynamical system after technology blockade
The influence of $\beta$ and $\varepsilon_F$ on the fixed point. $\rho = 10\%, \delta = 15\%$
Parameter values are fixed as $\rho = 10\%$ and $\delta = 15\%$. (a) The R&D efficiency of the leader and follower is $\varepsilon_L = 0.8$ and $\varepsilon_F = 0.6$. (a) The R&D efficiency of the leader and follower is $\varepsilon_L = 0.8$ and $\varepsilon_F = 0.7$
Parameter values are fixed as $\rho = 10\%$ and $\delta = 15\%$
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