American Institute of Mathematical Sciences

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

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

Elvio Accinelli 1, , Filipe Martins 2,, , Humberto Muñiz 3, , Bruno M. P. M. Oliveira 4,5, and  Alberto A. Pinto 2,6,

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.

Keywords: Economic policy, innovative firms, skilled labor, evolutionary dynamics, innovation cycles.
Mathematics Subject Classification: Primary: 91A22, 91B02, 91B55; Secondary: 91A06, 91A10, 91B66.
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.

Figure 1.  The dynamics on the edges of the cube
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Figure 2.  The innovation and traning (I&T) cycle
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Figure 3.  Bistability of the I&T poverty trap equilibrium $ (0,0,0) $ and the I&T ideal growth equilibrium $ (1,1,1) $
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Table 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}) $
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$ 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}) $
Table 2.  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}}) $
Table Options

Download as excel

$ 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}}) $
Table 3.  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} $
Table Options

Download as excel

$ 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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