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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 |
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 [
References:
[1] |
D. Acemoglu and J. A. Robinson,
Economic backwardness in political perspectives, Am. Polit. Sci. Rev., 100 (2006), 115-131.
|
[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. |
[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. |
[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. |
[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. |
[6] |
S. Becker,
A theory of competition among pressure groups for political influence, Q. J. Econ., 98 (1983), 371-400.
doi: 10.2307/1886017. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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.
|
[17] |
A. Gerschenkron,
Economic Backwardness in Historical Perspectives, Harvard University Press, 1962. |
[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. |
[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. |
[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.
|
[21] |
R. Musil, Der Mann ohne Eigenschaften, Rowohkt Verlag, Austria, 1930–1943. |
[22] |
L. Pareschi and G. Toscani,
Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, 2014. |
[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. |
[24] |
N. N. Taleb,
The Black Swan: The Impact of the Highly Improbable, Random House, New York City, 2007. |
[25] |
G. Toscani, Wealth redistribution in conservative linear kinetic models with taxation, Europhys. Lett., 88 (2009), 10007. |
show all references
References:
[1] |
D. Acemoglu and J. A. Robinson,
Economic backwardness in political perspectives, Am. Polit. Sci. Rev., 100 (2006), 115-131.
|
[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. |
[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. |
[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. |
[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. |
[6] |
S. Becker,
A theory of competition among pressure groups for political influence, Q. J. Econ., 98 (1983), 371-400.
doi: 10.2307/1886017. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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.
|
[17] |
A. Gerschenkron,
Economic Backwardness in Historical Perspectives, Harvard University Press, 1962. |
[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. |
[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. |
[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.
|
[21] |
R. Musil, Der Mann ohne Eigenschaften, Rowohkt Verlag, Austria, 1930–1943. |
[22] |
L. Pareschi and G. Toscani,
Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, 2014. |
[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. |
[24] |
N. N. Taleb,
The Black Swan: The Impact of the Highly Improbable, Random House, New York City, 2007. |
[25] |
G. Toscani, Wealth redistribution in conservative linear kinetic models with taxation, Europhys. Lett., 88 (2009), 10007. |











Parameter | Meaning |
positive return on the citizen wealth by means of the introduction of technological innovation | |
citizen susceptibility to change opinion | |
negative return on the political power of the ruler by means of the political power of the competing group |
Parameter | Meaning |
positive return on the citizen wealth by means of the introduction of technological innovation | |
citizen susceptibility to change opinion | |
negative return on the political power of the ruler by means of the political power of the competing group |
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