Escaping the trap of 'blocking': A kinetic model linking economic development and political competition

M. Dolfin; D. Knopoff; L. Leonida; D. Maimone Ansaldo Patti

doi:10.3934/krm.2017016

Article Contents

2017, Volume 10, Issue 2: 423-443. Doi: 10.3934/krm.2017016

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Escaping the trap of 'blocking': A kinetic model linking economic development and political competition

1.
Department of Engineering, University of Messina, Messina, Italy
2.
Centro de Investigación y Estudios de Matemática (CONICET) - FaMAF (UNC), Córdoba, Argentina
3.
School of Management and Business, King's College London, London, UK

* Corresponding author
* Corresponding author

Received: February 2016

Revised: July 2016

Published: May 2017

M.D. acknowledges a support by the University of Messina through the Research & Mobility 2015 Project (project code RES AND MOB 2015 DISTASO). D.K. acknowledges a support by the Indam (GNFM) through the Visiting Professor project 2015

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Abstract

In this paper we present a kinetic model with evolutive stochastic game-type interactions, analyzing the relationship between the level of political competition in a society and the degree of economic liberalization. The above issue regards the complex interactions between economy and institutional policies intended to introduce technological innovations in a society, where technological innovations are intended in a broad sense comprehending reforms critical to production [3]. A special focus is placed on the political replacement effect described in a macroscopic model by Acemoglu and Robinson (AR-model [1], henceforth), which can determine the phenomenon of innovation 'blocking', possibly leading to economic backwardness. One of the goals of our modelization is to obtain a mesoscopic dynamical model whose macroscopic outputs are qualitatively comparable with stylized facts of the AR-model and the comparison is settled in a number of case studies. A set of numerical solutions is presented showing the non monotonous relationship between economic liberalization and political competition in particular conditions, which can be considered as an emergent phenomenon of the analyzed complex socio-economic interaction dynamics.

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Mathematics Subject Classification: Primary: 91D10; Secondary: 91C99.

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Figure 1. Nonmonotonicity with 'blocking'

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Figure 2. Non monotonicity without 'blocking'

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Figure 3. Monotonicity without 'blocking'

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Figure 4. Computational analysis of first order moments evolution

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Figure 5. Initial conditions of the system

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Figure 6. Innovation function vs. time (left) and vs. the inverse of the political competition ($1-\mathbb E^3_\nu$) (right) in a society with strong rulers and weak opposition

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Figure 7. Time evolution of some significative marginal first moments of the distributions in the subpopulations (left) and the non monotonous relationship between the propensity to innovate of the rulers and the inverse of the political competition in the society

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Figure 8. Innovation function vs.time (left) and vs. the opposite of the political power of the competing group ($1-\mathbb E^3_\nu$) (right) for different parameter values

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Figure 9. Time evolution of the political power of the rulers, of the political power of the competing group and of the citizen wealth, for different parameter values

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Figure 10. Time evolution of the political power of the rulers, the political power of the competing group and the citizen wealth, in an initially poor society (left), and in an initially rich society (right)

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Figure 11. Evolution of the quantities F(t) (left) and G(t) (right)

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Table 1. Parameters involved in the transition probabilities

Parameter	Meaning
${\tilde{\alpha }}$	positive return on the citizen wealth by means of the introduction of technological innovation
$\beta $	citizen susceptibility to change opinion
${\tilde{\gamma }}$	negative return on the political power of the ruler by means of the political power of the competing group

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