# American Institute of Mathematical Sciences

November  2021, 26(11): 5723-5754. doi: 10.3934/dcdsb.2021180

## Firms, technology, training and government fiscal policies: An evolutionary approach

 1 Facultad de Economía, Universidad Autónoma de San Luis Potosí, México, álvaro Obregón 64, Col. Centro, C. P. 78000, San Luis Potosí, S.L.P., México 2 LIAAD–INESC TEC, Rua do Campo Alegre 687, 4169-007 Porto, Portugal 3 Insituto Potosino de Investigación científica y tecnológica A.C., México, Camino a la presa de San José 2055, Lomas 4ta secc, C.P. 78216, San Luis Potosí, S.L.P., México 4 Faculdade de Ciências da Nutrição e Alimentação, Universidade do Porto 5 LIAAD–INESC TEC, Rua do Campo Alegre 823, 4150-180 Porto, Portugal 6 Departmento de Matemática, Universidade do Porto, Portugal

*Corresponding author: Filipe Martins

Received  December 2020 Revised  May 2021 Published  November 2021 Early access  July 2021

In this paper we propose and analyze a game theoretical model regarding the dynamical interaction between government fiscal policy choices toward innovation and training (I&T), firm's innovation, and worker's levels of training and education. We discuss four economic scenarios corresponding to strict pure Nash equilibria: the government and I&T poverty trap, the I&T poverty trap, the I&T high premium niche, and the I&T ideal growth. The main novelty of this model is to consider the government as one of the three interacting players in the game that also allow us to analyse the I&T mixed economic scenarios with a unique strictly mixed Nash equilibrium and with I&T evolutionary dynamical cycles.

Citation: Elvio Accinelli, Filipe Martins, Humberto Muñiz, Bruno M. P. M. Oliveira, Alberto A. Pinto. Firms, technology, training and government fiscal policies: An evolutionary approach. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5723-5754. doi: 10.3934/dcdsb.2021180
##### References:
 [1] E. Accinelli, F. Martins, A. A. Pinto, A. Afsar and B. M. P. M. Oliveira, The power of voting and corruption cycles, The Journal of Mathematical Sociology, (2020), 1–24. doi: 10.1080/0022250X.2020.1818077. [2] E. Accinelli, B. Bazzano, F. Robledo and P. Romero, Nash equilibrium in evolutionary competitive models of firms and workers under external regulation, Journal of Dynamics & Games, 2 (2015), 1-32.  doi: 10.3934/jdg.2015.2.1. [3] E. Accinelli and E. J. S. Carrera, Strategic complementarities between innovative firms and skilled workers: The poverty trap and the policymaker's intervention, Structural Change and Economic Dynamics, 22 (2011), 30-40.  doi: 10.1016/j.strueco.2010.11.004. [4] E. Accinelli, E. S. Carrera, L. Policardo and O. Salas, Free mobility of capital and labor force in a two-country model: The dynamic game for growth, Journal of Dynamics & Games, 6 (2019), 179-194.  doi: 10.3934/jdg.2019013. [5] U. Akcigit, J. Grigsby, T. Nicholas and S. Stantcheva, Taxation and Innovation in the 20th Century, Technical report, National Bureau of Economic Research, 2018. [6] S. Aoyagi and S. Managi, The impact of subsidies on efficiency and production: Empirical test of forestry in Japan, International Journal of Agricultural Resources, Governance and Ecology, 3 (2004), 216-230.  doi: 10.1504/IJARGE.2004.006037. [7] C. N. Brunnschweiler and E. H. Bulte, Linking natural resources to slow growth and more conflict, Science, 320 (2008), 616-617.  doi: 10.1126/science.1154539. [8] E. H. Bulte, R. Damania and R. T. Deacon, Resource intensity, institutions, and development, World Development, 33 (2005), 1029-1044.  doi: 10.1016/j.worlddev.2005.04.004. [9] E. J. S. Carrera, S. Ille and G. Travaglini, Macrodynamic Modeling of Innovation Equilibria and Traps, The B.E. Journal of Macroeconomics, 2021. doi: 10.1515/bejm-2020-0258. [10] E. J. S. Carrera, L. Policardo, A. García and E. Accinelli, A co-evolutionary model for human capital and innovative firms, in Games and Dynamics in Economics Springer, (2020), 17–32. doi: 10.1007/978-981-15-3623-6_2. [11] V. Costantini and S. Monni, Environment, human development and economic growth, Ecological Economics, 64 (2008), 867-880.  doi: 10.1016/j.ecolecon.2007.05.011. [12] R. Feenstra, New technology and trade: A threat to low-skilled workers?, Swedish Economic Policy Review, 5 (1998), 137-160. [13] H. Fofack, Technology Trap and Poverty Trap in Sub-Saharan Africa, The World Bank, World Bank Institute, 2008. [14] D. Fudenberg and J. Tirole, Game Theory, MIT Press, Cambridge, MA, 1991. [15] V. Gunnella, L. Quaglietti, et al., The economic implications of rising protectionism: A euro area and global perspective, Economic Bulletin Articles, 3 (2019). [16] S. Helfstein, What Happens When Antitrust and Protectionism Cycles Collide, online, 2019. [17] International Labour Office, A skilled workforce for strong, sustainable and balanced growth: A G20 training strategy, 2010. [18] M. Khan, State failure in developing countries and strategies of institutional reform, Toward Pro-Poor Policies. Aid, Institutions, and Globalization. Annual World Bank Conference on Development Economics, Europe, Oxford University Press and World Bank, 2004,165–195. [19] L. Kim and J. M. Utterback, The evolution of organizational structure and technology in a developing country, Management Science, 29 (1983), 1185-1197.  doi: 10.1287/mnsc.29.10.1185. [20] C. F. Manski, Communicating uncertainty in policy analysis, Proceedings of the National Academy of Sciences, 116 (2019), 7634-7641.  doi: 10.1073/pnas.1722389115. [21] C. Pérez, La modernización industrial en américa latina y la herencia de la sustitución de importaciones, Comercio Exterior, 46 (1996), 347-363. [22] M. U. Rehman, N. Asghar and J. Hussain, Are disaggregate industrial returns sensitive to economic policy uncertainty, Physica A: Statistical Mechanics and its Applications, 527 (2019), 121301. doi: 10.1016/j.physa.2019.121301. [23] D. Rodrik, Industrial policy: Don't ask why, ask how, Middle East Development Journal, 1 (2009), 1-29.  doi: 10.1142/S1793812009000024. [24] P. M. Romer, Increasing returns and long-run growth, Journal of Political Economy, 94 (1986), 1002-1037.  doi: 10.1086/261420. [25] J. D. Sachs and A. M Warner, Natural Resource Abundance and Economic Growth, Technical report, National Bureau of Economic Research, 1995. [26] J. M. Salazar-Xirinachs, I. Nübler and R. Kozul-Wright, editors, Transforming Economies: Making Industrial Policy Work for Growth, Jobs and Development, International Labour Organization, 2014. [27] W. H. Sandholm, Population games and deterministic evolutionary dynamics, Handbook of Game Theory with Economic Applications, 4 (2015), 703-778.  doi: 10.1016/B978-0-444-53766-9.00013-6. [28] J. A. Schumpeter, The Theory of Economic Development: An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle, Transaction Books, New Brunswick, New Jersey, Translated from the 1911 original German, Theorie der wirtschaftlichen Entwicklung (translator: Redvers Opie), 1983. [29] S. Sorin, Replicator dynamics: Old and new, Journal of Dynamics & Games, 7 (2020), 365-386.  doi: 10.3934/jdg.2020028. [30] The Dutch Disease, The Economist, (1977), 82–83. [31] J. Tinbergen, Income Distribution: Analysis and Policies, Elsevier, 1975.

show all references

##### References:
 [1] E. Accinelli, F. Martins, A. A. Pinto, A. Afsar and B. M. P. M. Oliveira, The power of voting and corruption cycles, The Journal of Mathematical Sociology, (2020), 1–24. doi: 10.1080/0022250X.2020.1818077. [2] E. Accinelli, B. Bazzano, F. Robledo and P. Romero, Nash equilibrium in evolutionary competitive models of firms and workers under external regulation, Journal of Dynamics & Games, 2 (2015), 1-32.  doi: 10.3934/jdg.2015.2.1. [3] E. Accinelli and E. J. S. Carrera, Strategic complementarities between innovative firms and skilled workers: The poverty trap and the policymaker's intervention, Structural Change and Economic Dynamics, 22 (2011), 30-40.  doi: 10.1016/j.strueco.2010.11.004. [4] E. Accinelli, E. S. Carrera, L. Policardo and O. Salas, Free mobility of capital and labor force in a two-country model: The dynamic game for growth, Journal of Dynamics & Games, 6 (2019), 179-194.  doi: 10.3934/jdg.2019013. [5] U. Akcigit, J. Grigsby, T. Nicholas and S. Stantcheva, Taxation and Innovation in the 20th Century, Technical report, National Bureau of Economic Research, 2018. [6] S. Aoyagi and S. Managi, The impact of subsidies on efficiency and production: Empirical test of forestry in Japan, International Journal of Agricultural Resources, Governance and Ecology, 3 (2004), 216-230.  doi: 10.1504/IJARGE.2004.006037. [7] C. N. Brunnschweiler and E. H. Bulte, Linking natural resources to slow growth and more conflict, Science, 320 (2008), 616-617.  doi: 10.1126/science.1154539. [8] E. H. Bulte, R. Damania and R. T. Deacon, Resource intensity, institutions, and development, World Development, 33 (2005), 1029-1044.  doi: 10.1016/j.worlddev.2005.04.004. [9] E. J. S. Carrera, S. Ille and G. Travaglini, Macrodynamic Modeling of Innovation Equilibria and Traps, The B.E. Journal of Macroeconomics, 2021. doi: 10.1515/bejm-2020-0258. [10] E. J. S. Carrera, L. Policardo, A. García and E. Accinelli, A co-evolutionary model for human capital and innovative firms, in Games and Dynamics in Economics Springer, (2020), 17–32. doi: 10.1007/978-981-15-3623-6_2. [11] V. Costantini and S. Monni, Environment, human development and economic growth, Ecological Economics, 64 (2008), 867-880.  doi: 10.1016/j.ecolecon.2007.05.011. [12] R. Feenstra, New technology and trade: A threat to low-skilled workers?, Swedish Economic Policy Review, 5 (1998), 137-160. [13] H. Fofack, Technology Trap and Poverty Trap in Sub-Saharan Africa, The World Bank, World Bank Institute, 2008. [14] D. Fudenberg and J. Tirole, Game Theory, MIT Press, Cambridge, MA, 1991. [15] V. Gunnella, L. Quaglietti, et al., The economic implications of rising protectionism: A euro area and global perspective, Economic Bulletin Articles, 3 (2019). [16] S. Helfstein, What Happens When Antitrust and Protectionism Cycles Collide, online, 2019. [17] International Labour Office, A skilled workforce for strong, sustainable and balanced growth: A G20 training strategy, 2010. [18] M. Khan, State failure in developing countries and strategies of institutional reform, Toward Pro-Poor Policies. Aid, Institutions, and Globalization. Annual World Bank Conference on Development Economics, Europe, Oxford University Press and World Bank, 2004,165–195. [19] L. Kim and J. M. Utterback, The evolution of organizational structure and technology in a developing country, Management Science, 29 (1983), 1185-1197.  doi: 10.1287/mnsc.29.10.1185. [20] C. F. Manski, Communicating uncertainty in policy analysis, Proceedings of the National Academy of Sciences, 116 (2019), 7634-7641.  doi: 10.1073/pnas.1722389115. [21] C. Pérez, La modernización industrial en américa latina y la herencia de la sustitución de importaciones, Comercio Exterior, 46 (1996), 347-363. [22] M. U. Rehman, N. Asghar and J. Hussain, Are disaggregate industrial returns sensitive to economic policy uncertainty, Physica A: Statistical Mechanics and its Applications, 527 (2019), 121301. doi: 10.1016/j.physa.2019.121301. [23] D. Rodrik, Industrial policy: Don't ask why, ask how, Middle East Development Journal, 1 (2009), 1-29.  doi: 10.1142/S1793812009000024. [24] P. M. Romer, Increasing returns and long-run growth, Journal of Political Economy, 94 (1986), 1002-1037.  doi: 10.1086/261420. [25] J. D. Sachs and A. M Warner, Natural Resource Abundance and Economic Growth, Technical report, National Bureau of Economic Research, 1995. [26] J. M. Salazar-Xirinachs, I. Nübler and R. Kozul-Wright, editors, Transforming Economies: Making Industrial Policy Work for Growth, Jobs and Development, International Labour Organization, 2014. [27] W. H. Sandholm, Population games and deterministic evolutionary dynamics, Handbook of Game Theory with Economic Applications, 4 (2015), 703-778.  doi: 10.1016/B978-0-444-53766-9.00013-6. [28] J. A. Schumpeter, The Theory of Economic Development: An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle, Transaction Books, New Brunswick, New Jersey, Translated from the 1911 original German, Theorie der wirtschaftlichen Entwicklung (translator: Redvers Opie), 1983. [29] S. Sorin, Replicator dynamics: Old and new, Journal of Dynamics & Games, 7 (2020), 365-386.  doi: 10.3934/jdg.2020028. [30] The Dutch Disease, The Economist, (1977), 82–83. [31] J. Tinbergen, Income Distribution: Analysis and Policies, Elsevier, 1975.
The dynamics on the edges of the cube
The innovation and traning (I&T) cycle
Bistability of the I&T poverty trap equilibrium $(0,0,0)$ and the I&T ideal growth equilibrium $(1,1,1)$
Payoff table of the government
 $I,S$ $I,\overline{S}$ $\overline{I},S$ $\overline{I},\overline{S}$ $G$ $\tau_I\pi_{I}(S) -T$ $\tau_I\pi_{I}(\overline{S})$ $\tau_{\overline{ I}}\pi_{\overline{ I}}(S)-T$ $\tau_{\overline{ I}}\pi_{\overline{ I}}(\overline{S})$ $\overline{G}$ $\overline{\tau}\pi_{I}(S)$ $\overline{\tau}\pi_{I}(\overline{S})$ $\overline{\tau}\pi_{\overline{I}}(S)$ $\overline{\tau}\pi_{\overline{I}}(\overline{S})$
 $I,S$ $I,\overline{S}$ $\overline{I},S$ $\overline{I},\overline{S}$ $G$ $\tau_I\pi_{I}(S) -T$ $\tau_I\pi_{I}(\overline{S})$ $\tau_{\overline{ I}}\pi_{\overline{ I}}(S)-T$ $\tau_{\overline{ I}}\pi_{\overline{ I}}(\overline{S})$ $\overline{G}$ $\overline{\tau}\pi_{I}(S)$ $\overline{\tau}\pi_{I}(\overline{S})$ $\overline{\tau}\pi_{\overline{I}}(S)$ $\overline{\tau}\pi_{\overline{I}}(\overline{S})$
Payoff table of a firm
 $G,S$ $G,\overline{S}$ $\overline{G},S$ $\overline{G},\overline{S}$ $I$ $(1-\tau_I)\pi_I(S)$ $(1-\tau_I)\pi_I({\overline{S}})$ $(1-\overline{\tau})\pi_I(S)$ $(1-\overline{\tau})\pi_I({\overline{S}})$ $\overline{I}$ $(1-\tau_{\overline{I}})\pi_{\overline{I}}(S)$ $(1-\tau_{\overline{I}})\pi_{\overline{I}}({\overline{S}})$ $(1-\overline{\tau})\pi_{\overline{I}}(S)$ $(1-\overline{\tau})\pi_{\overline{I}}({\overline{S}})$
 $G,S$ $G,\overline{S}$ $\overline{G},S$ $\overline{G},\overline{S}$ $I$ $(1-\tau_I)\pi_I(S)$ $(1-\tau_I)\pi_I({\overline{S}})$ $(1-\overline{\tau})\pi_I(S)$ $(1-\overline{\tau})\pi_I({\overline{S}})$ $\overline{I}$ $(1-\tau_{\overline{I}})\pi_{\overline{I}}(S)$ $(1-\tau_{\overline{I}})\pi_{\overline{I}}({\overline{S}})$ $(1-\overline{\tau})\pi_{\overline{I}}(S)$ $(1-\overline{\tau})\pi_{\overline{I}}({\overline{S}})$
Payoff table of workers
 $G,I$ $G,\overline{I}$ $\overline{G},I$ $\overline{G},\overline{I}$ $S$ $s + p - C + T$ $s - C +T$ $s + p - C$ $s - C$ $\overline{S}$ $\overline{s}+\overline{p}$ $\overline{s}$ $\overline{s}+\overline{p}$ $\overline{s}$
 $G,I$ $G,\overline{I}$ $\overline{G},I$ $\overline{G},\overline{I}$ $S$ $s + p - C + T$ $s - C +T$ $s + p - C$ $s - C$ $\overline{S}$ $\overline{s}+\overline{p}$ $\overline{s}$ $\overline{s}+\overline{p}$ $\overline{s}$
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