The economophysical model of the propagation of innovation: the Ising model

The process of technical and economic justification of investment, analysis and evaluation of the effectiveness of innovation requires a tool for describing and modeling the process of distribution of technology in the industry. The work presents a model of propagation of innovation involving physical approaches, describing the market saturation point, i.e. the point at which the exponential growth of the innovation propagation speed is replaced by the logarithmic growth. The object of the study is the propagation of innovation, and the subject is the development of the market saturation point functional. The authors justified the implementation and described the approach to modeling of the process of saturation of the market with innovation by the physical Ising model. The value of the Ising model’s toolkit is presented by the Curie point in ferromagnets which characterizes the second order phase transition. The article presents the mathematical model of the compliance of physical parameters with economic ones: the amount of inter-company influence, barriers to implementation and breakthrough of innovation. The authors adduce the discussion of the limitations and applicability of this model as well as further potential directions of study of economophysical models. The tools developed by the authors can be used in all sectors of economics to improve their innovation activity level.

1. World Intellectual property Organization. Global Innovation Index. Available at: https://www.wipo.int/global_innovation_index/en/2023/ (accessed on 27.08.2024).

2. Costello D.M. A cross-country, cross-industry comparison of productivity growth. The Journal of Political Economy. 1993;101(2):207–222. https://doi.org/10.1086/261873

3. Solow R.M. Technical change and the aggregate production function. The Review of Economics and Statistics. 1957;39(3):312–320. https://doi.org/10.2307/1926047

4. Harberger A.C. A vision of the growth process. The American Economic Review. 1998;88(1):1–32. Available at: http://www.econ.ucla.edu/harberger/vision.pdf

5. Chirwa T., Odhiambo N. Exogenous and endogenous growth models: a critical review. Comparative Economic Research. Central and Eastern Europe. 2018;21(4):63–84. https://doi.org/10.2478/cer2018-0027

6. Hagerstrand T. Innovation diffusion as a spatial process. Chicago: University of Chicago Press; 1967. 334 p.

7. Zemtsov S., Baburin V. Modeling of diffusion of innovation and typology of Russian regions: A case study of cellular communication. Izvestiya Rossiiskoi Akademii Nauk. Seriya Geograficheskaya. 2017;(4):17–30. (In Russ.). https://doi.org/10.7868/S0373244417100024

8. Rogers E.M. Diffusion of innovations. NY: The Free Press; 1983. 447 p.

9. Bass F.M. A new product growth for model consumer durables. Management Science. 1969;15(5):215–227. https://doi.org/10.1287/mnsc.15.5.215

10. Fisher J.C., Pry R.H. A simple substitution model of technological change. Technological Forecasting and Social Change. 1971–1972;3:75–88. https://doi.org/10.1016/S0040-1625(71)80005-7

11. Norton J.A., Bass F.M. A diffusion theory model of adoption and substitution for successive generations of high-technology products. Management Science. 1987;33(9):1069–1086. https://doi.org/10.1287/MNSC.33.9.1069

12. Kumar N. Review of innovation diffusion models; 2015. No 1/2015-01. 54 p. https://doi.org/10.13140/RG.2.1.2413.0728

13. Sadovnichiy V.A., Akaev A.A., Ilyin I.V., Korotaev A.V., Malkov S.Yu. Modeling and forecasting of global dynamics in the XXI century. Vestnik Moskovskogo universiteta. Seriya 27: Globalistika i geopolitika. 2022;(1):5–35. (In Russ.). https://doi.org/10.56429/2414-4894-2022-39-1-5-35

14. Griliches Z. Research costs and social returns: hybrid corn and related innovations. Journal of Political Economy. 1958;66(5):419. https://doi.org/10.1086/258077

15. Mansfield E. Technical change and the rate of imitation. Econometrica. 1961;29(4):741–766. https://doi.org/10.2307/1911817

16. Dixon R. Hybrid corn revisited. Econometrica. 1980;48(6):1451–1461. https://doi.org/10.2307/1912817

17. Dinar A., Marom D. Rate and patterns of computer adoption and use in agricultural extensions. Technological Forecasting and Social Change. 1991;39(3):309–318. https://doi.org/10.1016/0040-1625(91)90043-f

18. Soete L. International diffusion of technology, industrial development and technological leapfrogging. World Development. 1985;13(3):409–422. https://doi.org/10.1016/0305-750X(85)90138-X

19. Kelley M.R. External learning opportunities and the diffusion of process innovations to small firms. The case of programmable automation. Technological Forecasting and Social Change. 1991;39(1-2):103–125.

20. Franck B., Gaussens O. L’automatisation des petites et moyennes entreprises: une étude économetrique. Économie & Prévision. 1992;(102-103):37–54. Available at: https://www.persee.fr/doc/ecop_0249-4744_1992_num_102_1_5274

21. O’Farrell P.N., Oakey R.P. Regional variations in the adoption of CNC machine tools by small engineering firms: a multivariate analysis. Environment and Planning A. 1992;24(6):887–902.

22. Karshenas M., Stoneman P. Rank, stock, order and epidemic effects in the diffusion of new process technologies: An empirical model. RAND Journal of Economics. 1993;24(4):503–528.

23. Lancaster T. Econometric methods for the duration of unemployment. Econometrica. 1979;47(4):939–956. https://doi.org/10.2307/1914140

24. Shimogawa S., Shinno M., Saito H. Structure of S-shaped growth in innovation diffusion. Physical Review E. 2012;85(5):056121. https://doi.org/10.1103/PhysRevE.85.056121

25. Battisti G., Hollenstein H., Stoneman P., Woerter M. Inter and intra firm diffusion of ICT in the United Kingdom (UK) and Switzerland (CH): An internationally comparative study based on firm-level data. Economics of Innovation and New Technology. 2007;16:669–687.

26. David P. Zvi Griliches and the economics of technology diffusion: Adoption of innovations, investment lags, and productivity growth – “Connecting the Dots”. Discussion paper 09-016; 2010. 76 p. Available at: https://www.researchgate.net/publication/254450764_Zvi_Griliches_and_the_Economics_of_Technology_Diffusion_Adoption_of_Innovations_Investment_Lags_and_Productivity_Growth

27. Stoneman P., Toivanen O. Technological diffusion, uncertainty and irreversibility: The international diffusion of industrial robots; 2000. 32 p. Available at: www.researchgate.net/publication/228827358_Technological_Diffusion_Uncertainty_and_Irreversibility_The_International_Diffusion_of_Industrial_Robots

28. Laciana C.E., Rovere S.L. Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies. Physica A: Statistical Mechanics and its Applications. 2011;390(6):1139–1149. https://doi.org/10.1016/j.physa.2010.11.006

29. Stiglitz J.E. Learning to learn, localized learning and technological progress. In: Dasgupta P., Stoneman P. (eds.). Economic policy and technological change. Cambridge University Press; 1987. P. 125–153. https://doi.org/10.1017/CBO9780511559938.007

30. David P. Technical choice, innovation and economic growth. London: Cambridge University Press; 1975. 334 p.

31. Mansfield E. Industrial research and technological innovation. NY: Norton; 1968. 235 p.

32. Romeo A.A. The rate of imitation of a capital-embodied process innovation. Economica. 1977;44(173):63–69. https://doi.org/10.2307/2553550

33. Lyinn L. New data on the diffusion of the basic oxygen furnces in the U.S. and Japan. Journal of Industrial Economics. 1981;30(2):123–135.

34. Arcangeli F., Dosi G., Moggi M. Patterns of diffusion of electronic technologies: An international comparison with special reference to the Italian case. Research Policy. 1991;20(6):515–529.

35. Mansfield E. The diffusion of industrial robots in Japan and the United States. Research Policy. 1989;18(4):183–192.

36. Ovsyannikov I.R., Zhdaneev O.V. Forecast of innovative activity in key areas of energy transition technologies based on analysis of patent activity. International Journal of Hydrogen Energy. 2024;87:1261–1276. https://doi.org/10.1016/j.ijhydene.2024.08.375

37. Rosegger G. Diffusion through interfirm cooperation. A case study. Technological Forecasting and Social Change. 1991;39(1-2):81–103.

38. Zhdaneev O.V., Ovsyannikov I.R. Influence of external factors on innovation activity of fuel and energy companies. Studies on Russian Economic Development. 2024;35(2):208–214. https://doi.org/10.1134/S1075700724020175

39. Zhdaneev O.V., Frolov K.N. Technological and institutional priorities of the oil and gas complex of the Russian Federation in the term of the world energy transition. International Journal of Hydrogen Energy. 2024;58:1418–1428. https://doi.org/10.1016/j.ijhydene.2024.01.285