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June  2017, 10(2): 423-443. doi: 10.3934/krm.2017016

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

M. Dolfin 1,, , D. Knopoff 2, , L. Leonida 3, and  D. Maimone Ansaldo Patti 1,

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

Received  February 2016 Revised  July 2016 Published  November 2016

Fund Project: 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.

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.

Keywords: Political economy, technological innovation, political competition, interacting subpopulations, kinetic theory.
Mathematics Subject Classification: Primary: 91D10; Secondary: 91C99.
Citation: M. Dolfin, D. Knopoff, L. Leonida, D. Maimone Ansaldo Patti. Escaping the trap of 'blocking': A kinetic model linking economic development and political competition. Kinetic & Related Models, 2017, 10 (2) : 423-443. doi: 10.3934/krm.2017016
References:
[1]

D. Acemoglu and J. A. Robinson, Economic backwardness in political perspectives, Am. Polit. Sci. Rev., 100 (2006), 115-131.   Google Scholar

[2]

D. Acemoglu and J. A. Robinson, Political losers as a barrier to economic development, Am. Econ. Rev., Papers and Proceedings, 90 (2000), 126-130.  doi: 10.1257/aer.90.2.126.  Google Scholar

[3]

D. Acemoglu, Localised and biased technologies: Atkinson and Stiglitz's new view, induced innovations and directed technological change, The Economic Journal, 125 (2015), 443-463.  doi: 10.1111/ecoj.12227.  Google Scholar

[4]

G. Ajmone Marsan, N. Bellomo and L. Gibelli, Stochastic evolving differential games toward a systems theory of behavioral social dynamics, Math. Models Methods Appl. Sci., 26 (2016), 1051-1093.  doi: 10.1142/S0218202516500251.  Google Scholar

[5]

J. Banasiak and M. Lachowiz, Methods of Small Parameter in Mathematical Biology Series Modeling and simulation in Science, Engineering and Technology, Birkhäuser, 2014. doi: 10.1007/978-3-319-05140-6.  Google Scholar

[6]

S. Becker, A theory of competition among pressure groups for political influence, Q. J. Econ., 98 (1983), 371-400.  doi: 10.2307/1886017.  Google Scholar

[7]

N. Bellomo, D. Knopoff and J. Soler, On the difficult interplay between life, ''complexity'', and mathematical sciences, Math. Models Methods Appl. Sci., 23 (2013), 1861-1913.  doi: 10.1142/S021820251350053X.  Google Scholar

[8]

N. Bellomo, F. Colasuonno, D. Knopoff and J. Soler, From systems theory of sociology to modeling the onset and evolution of criminality, Netw. Heterog. Media, 10 (2015), 421-441.  doi: 10.3934/nhm.2015.10.421.  Google Scholar

[9]

N. Bellomo, M. A. Herrero and A. Tosin, On the dynamics of social conflicts looking for the Black Swan, Kinet. Relat. Models, 6 (2013), 459-479.  doi: 10.3934/krm.2013.6.459.  Google Scholar

[10]

T. Besley, T. Persson and D. M. Sturm, Political Competition, Policy and Growth: Theory and Evidence from the US, Rev. Econom. Stud., 77 (2010), 1329-1352.  doi: 10.1111/j.1467-937X.2010.00606.x.  Google Scholar

[11]

M. Dolfin and M. Lachowicz, Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions, Math. Models Methods Appl. Sci., 24 (2014), 2361-2381.  doi: 10.1142/S0218202514500237.  Google Scholar

[12]

M. Dolfin and M. Lachowicz, Modeling opinion dynamics: How the network enhances consensus, Netw. Heterog. Media, 10 (2015), 877-896.  doi: 10.3934/nhm.2015.10.877.  Google Scholar

[13]

M. Dolfin and M. Lachowicz, Modeling DNA thermal denaturation at the mesoscopic level, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 2469-2482.  doi: 10.3934/dcdsb.2014.19.2469.  Google Scholar

[14]

B. During and G. Toscani, International and domestic trading and wealth distribution, Commun. Math. Sci., 6 (2008), 1043-1058.  doi: 10.4310/CMS.2008.v6.n4.a12.  Google Scholar

[15]

B. During, D. Matthes and G. Toscani, Kinetic equations modelling wealth redistribution: A comparison of approaches Phys. Rev. E 78 (2008), 056103, 12pp. doi: 10.1103/PhysRevE.78.056103.  Google Scholar

[16]

B. During, D. Matthes and G. Toscani, A Boltzmann-type approach to the formation of wealth distribution curves, (Notes of the Porto Ercole School, June 2008), Riv. Mat. Univ. Parma, 8 (2009), 199-261.   Google Scholar

[17]

A. Gerschenkron, Economic Backwardness in Historical Perspectives, Harvard University Press, 1962. Google Scholar

[18]

D. Helbing, Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes Ⅱ Ed., Springer, 2010. doi: 10.1007/978-3-642-11546-2.  Google Scholar

[19]

D. Knopoff, On a mathematical theory of complex systems on networks with application to opinion formation, Math. Models Methods Appl. Sci., 24 (2014), 405-426.  doi: 10.1142/S0218202513400137.  Google Scholar

[20]

L. Leonida, D. Maimone Ansaldo Patti and P. Navarra, Testing the political replacement effect: A Panel Data Analysis, Oxford B. Econ. Stat., 75 (2013), 785-805.   Google Scholar

[21]

R. Musil, Der Mann ohne Eigenschaften, Rowohkt Verlag, Austria, 1930–1943. Google Scholar

[22]

L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, 2014. Google Scholar

[23]

L. Pareschi and G. Toscani, Self-similarity and power-like tails in non-conservative kinetic models, J. Stat. Phys., 124 (2006), 747-779.  doi: 10.1007/s10955-006-9025-y.  Google Scholar

[24]

N. N. Taleb, The Black Swan: The Impact of the Highly Improbable, Random House, New York City, 2007. Google Scholar

[25]

G. Toscani, Wealth redistribution in conservative linear kinetic models with taxation, Europhys. Lett., 88 (2009), 10007. Google Scholar

show all references

References:
[1]

D. Acemoglu and J. A. Robinson, Economic backwardness in political perspectives, Am. Polit. Sci. Rev., 100 (2006), 115-131.   Google Scholar

[2]

D. Acemoglu and J. A. Robinson, Political losers as a barrier to economic development, Am. Econ. Rev., Papers and Proceedings, 90 (2000), 126-130.  doi: 10.1257/aer.90.2.126.  Google Scholar

[3]

D. Acemoglu, Localised and biased technologies: Atkinson and Stiglitz's new view, induced innovations and directed technological change, The Economic Journal, 125 (2015), 443-463.  doi: 10.1111/ecoj.12227.  Google Scholar

[4]

G. Ajmone Marsan, N. Bellomo and L. Gibelli, Stochastic evolving differential games toward a systems theory of behavioral social dynamics, Math. Models Methods Appl. Sci., 26 (2016), 1051-1093.  doi: 10.1142/S0218202516500251.  Google Scholar

[5]

J. Banasiak and M. Lachowiz, Methods of Small Parameter in Mathematical Biology Series Modeling and simulation in Science, Engineering and Technology, Birkhäuser, 2014. doi: 10.1007/978-3-319-05140-6.  Google Scholar

[6]

S. Becker, A theory of competition among pressure groups for political influence, Q. J. Econ., 98 (1983), 371-400.  doi: 10.2307/1886017.  Google Scholar

[7]

N. Bellomo, D. Knopoff and J. Soler, On the difficult interplay between life, ''complexity'', and mathematical sciences, Math. Models Methods Appl. Sci., 23 (2013), 1861-1913.  doi: 10.1142/S021820251350053X.  Google Scholar

[8]

N. Bellomo, F. Colasuonno, D. Knopoff and J. Soler, From systems theory of sociology to modeling the onset and evolution of criminality, Netw. Heterog. Media, 10 (2015), 421-441.  doi: 10.3934/nhm.2015.10.421.  Google Scholar

[9]

N. Bellomo, M. A. Herrero and A. Tosin, On the dynamics of social conflicts looking for the Black Swan, Kinet. Relat. Models, 6 (2013), 459-479.  doi: 10.3934/krm.2013.6.459.  Google Scholar

[10]

T. Besley, T. Persson and D. M. Sturm, Political Competition, Policy and Growth: Theory and Evidence from the US, Rev. Econom. Stud., 77 (2010), 1329-1352.  doi: 10.1111/j.1467-937X.2010.00606.x.  Google Scholar

[11]

M. Dolfin and M. Lachowicz, Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions, Math. Models Methods Appl. Sci., 24 (2014), 2361-2381.  doi: 10.1142/S0218202514500237.  Google Scholar

[12]

M. Dolfin and M. Lachowicz, Modeling opinion dynamics: How the network enhances consensus, Netw. Heterog. Media, 10 (2015), 877-896.  doi: 10.3934/nhm.2015.10.877.  Google Scholar

[13]

M. Dolfin and M. Lachowicz, Modeling DNA thermal denaturation at the mesoscopic level, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 2469-2482.  doi: 10.3934/dcdsb.2014.19.2469.  Google Scholar

[14]

B. During and G. Toscani, International and domestic trading and wealth distribution, Commun. Math. Sci., 6 (2008), 1043-1058.  doi: 10.4310/CMS.2008.v6.n4.a12.  Google Scholar

[15]

B. During, D. Matthes and G. Toscani, Kinetic equations modelling wealth redistribution: A comparison of approaches Phys. Rev. E 78 (2008), 056103, 12pp. doi: 10.1103/PhysRevE.78.056103.  Google Scholar

[16]

B. During, D. Matthes and G. Toscani, A Boltzmann-type approach to the formation of wealth distribution curves, (Notes of the Porto Ercole School, June 2008), Riv. Mat. Univ. Parma, 8 (2009), 199-261.   Google Scholar

[17]

A. Gerschenkron, Economic Backwardness in Historical Perspectives, Harvard University Press, 1962. Google Scholar

[18]

D. Helbing, Quantitative Sociodynamics. Stochastic Methods and Models of Social Interaction Processes Ⅱ Ed., Springer, 2010. doi: 10.1007/978-3-642-11546-2.  Google Scholar

[19]

D. Knopoff, On a mathematical theory of complex systems on networks with application to opinion formation, Math. Models Methods Appl. Sci., 24 (2014), 405-426.  doi: 10.1142/S0218202513400137.  Google Scholar

[20]

L. Leonida, D. Maimone Ansaldo Patti and P. Navarra, Testing the political replacement effect: A Panel Data Analysis, Oxford B. Econ. Stat., 75 (2013), 785-805.   Google Scholar

[21]

R. Musil, Der Mann ohne Eigenschaften, Rowohkt Verlag, Austria, 1930–1943. Google Scholar

[22]

L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, 2014. Google Scholar

[23]

L. Pareschi and G. Toscani, Self-similarity and power-like tails in non-conservative kinetic models, J. Stat. Phys., 124 (2006), 747-779.  doi: 10.1007/s10955-006-9025-y.  Google Scholar

[24]

N. N. Taleb, The Black Swan: The Impact of the Highly Improbable, Random House, New York City, 2007. Google Scholar

[25]

G. Toscani, Wealth redistribution in conservative linear kinetic models with taxation, Europhys. Lett., 88 (2009), 10007. Google Scholar

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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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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