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doi: 10.3934/dcdsb.2021180
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## 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 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 & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021180
##### References:

show all references

##### References:
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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