On optimal leader’s investments strategy in a cyclic model of innovation race with random inventions times. (English) Zbl 1457.91205

Summary: In this paper, we develop a new dynamic model of optimal investments in R&D and manufacturing for a technological leader competing with a large number of identical followers on the market of a technological product. The model is formulated in the form of the infinite time horizon stochastic optimization problem. The evolution of new generations of the product is treated as a Poisson-type cyclic stochastic process. The technology spillovers effect acts as a driving force of technological change. We show that the original probabilistic problem that the leader is faced with can be reduced to a deterministic one. This result makes it possible to perform analytical studies and numerical calculations. Numerical simulations and economic interpretations are presented as well.


91B38 Production theory, theory of the firm
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
91B70 Stochastic models in economics
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[1] Kuhn, T.; ; The Structure of Scientific Revolutions: Chicago, IL, USA 1970; .
[2] Dosi, G.; Technological paradigms and technological trajectories; Res. Policy: 1982; Volume 11 ,147-162.
[3] Victor, N.M.; DRAMs as model organisms for study of technological evolution; Technol. Forecast. Social Chang.: 2002; Volume 69 ,243-262.
[4] Mukoyama, T.; Innovation, imitation, and growth with cumulative technology; J. Monet. Econ.: 2003; Volume 50 ,361-380.
[5] Porter, M.; ; Competitive Advantage: Creating and Sustaining Superior Performance: New York, NY, USA 1985; .
[6] Levin, R.C.; Klevorick, A.K.; Nelson, R.R.; Winter, S.G.; Appropriating the returns form industrial research and development; Brook. Pap. Econ. Act.: 1987; Volume 3 ,839-916.
[7] Teece, D.J.; Profiting from technological innovation: implications for integration, collaboration, licensing and public policy; Res. Policy: 1986; Volume 15 ,285-306.
[8] Goto, A.; Nagata, A.; ; Appropiability of Innovation and Technological Opportunity: Tokyo, Japan 1997; .
[9] Mansfield, E.; Schwartz, M.; Wagner, S.; Imitation costs and patents: an empirical study; Econ. J.: 1981; Volume 91 ,907-918.
[10] Lieberman, M.B.; Montgomery, D.B.; First-mover advantages; Strateg. Manag. J.: 1988; Volume 9 ,41-58.
[11] Ishida, M.; Matsumara, T.; Matsushima, N.; Market competition, R&D and firm profits in asymmetric oligopoly; J. Ind. Econ.: 2011; Volume 59 ,484-505.
[12] Ofek, E.; Sarvary, M.; R&D, marketing, and the success of next-generation products; Mark. Sci.: 2003; Volume 22 ,355-370.
[13] Parra, Á.; Sequential innovation, patent policy, and the dynamics of the replacement effect; RAND J. Econ.: 2019; Volume 50 ,568-590.
[14] Cohen, M.A.; Eliashberg, J.; Ho, T.-H.; New product development: The performance and time-to-market trade off; Manag. Sci.: 1996; Volume 42 ,173-186. · Zbl 0881.90081
[15] Bayus, B.L.; Speed-to-market and new product performance trade-offs; J. Prod. Manag.: 1997; Volume 14 ,485-497.
[16] Morgan, L.O.; Morgan, R.M.; Moore, W.L.; Quality and time-to-market trade-offs when there are multiple product generations; Manuf. Serv. Oper. Manag.: 2001; Volume 3 ,89-104.
[17] Cohen, M.A.; Eliashberg, J.; Ho, T.-H.; An anatomy of a decision-support system for developing and launching line extensions; J. Mark. Res.: 1997; Volume 34 ,117-129.
[18] Ramdas, K.; Swahney, M.S.; A cross-functional approach to evaluating multiple line extensions for assembled products; Manag. Sci.: 2001; Volume 47 ,22-36.
[19] Paulson Gjerde, K.A.; Slotnick, S.A.; Sobel, M.J.; New product innovation with multiple features and technology constraints; Manag. Sci.: 2002; Volume 48 ,1268-1284.
[20] Souza, G.C.; Bayus, B.L.; Wagner, H.M.; New-product strategy and industry clockspeed; Manag. Sci.: 2004; Volume 50 ,537-549.
[21] Reinganum, J.F.; On the diffusion of new technology: A game theoretic approach; Rev. Econ. Stud.: 1981; Volume 48 ,395-405. · Zbl 0493.90023
[22] Breitmoser, Y.; Tan, J.H.W.; Zizzo, D.J.; Understanding perpetual R&D races; Econ. Theory: 2010; Volume 44 ,445-567. · Zbl 1195.91019
[23] Aghion, P.; Howitt, P.; A model of growth through creative destruction; Econometrica: 1992; Volume 60 ,323-351. · Zbl 0825.90147
[24] Aghion, P.; Bechtold, S.; Cassar, L.; Herz, H.; The causal effects of competition on innovation: experimental evidence; J. Law Econ. Organ.: 2018; Volume 34 ,162-195.
[25] Meissner, D.; Kotsemir, M.; Conceptualizing the innovation process towards the “active innovation paradigm”—Trends and outlook; J. Innov. Entrep.: 2016; Volume 5 ,1-18.
[26] Morone, P.; Taylor, R.; ; Knowledge Diffusion and Innovation. Modelling Complex Entrepreneurial Behaviours: Cheltenham, UK 2010; .
[27] Arrow, K.J.; Kurz, M.; ; Public Investment, the Rate of Return and Optimal Fiscal Policy: Baltimore, MD, USA 1970; .
[28] Baro, R.; Sala-i-Martin, X.; ; Economic Growth: New York, NY, USA 1995; .
[29] Grossman, G.M.; Helpman, E.; ; Innovation and Growth in the Global Economy: Cambridge, MA, USA 1991; .
[30] Carlson, D.A.; Haurie, A.B.; Leizarowitz, A.; ; Infinite Horizon Optimal Control: Determenistic and Stochastic Systems: Berlin, Germany 1991; . · Zbl 0758.49001
[31] Galbraith, J.R.; ; Designing the Innovating Organization: Los Angeles, CA, USA 1999; .
[32] Gnedenko, B.V.; ; The Theory of Probability: New York, NY, USA 1962; .
[33] Intriligator, M.; ; Mathematical Optimization and Economic Theory: New York, NY, USA 1971; . · Zbl 1140.90302
[34] Winter, S.G.; Kaniovski, Y.M.; Dosi, G.; Modeling industrial dynamics with innovative entrants; Struct. Econ. Dyn.: 2000; Volume 11 ,255-293.
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