Figure 1.
Nonmonotonicity with 'blocking'
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2017, 10(2): 423-443.
doi: 10.3934/krm.2017016
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 [
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 and 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.
|
| [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. |
Figure 2.
Non monotonicity without 'blocking'
Figure 3.
Monotonicity without 'blocking'
Figure 4.
Computational analysis of first order moments evolution
Figure 5.
Initial conditions of the system
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
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
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
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
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)
Figure 11.
Evolution of the quantities F(t) (left) and G(t) (right)
Table 1.
Parameters involved in the transition probabilities
| 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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