# American Institute of Mathematical Sciences

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

 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.

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.
Nonmonotonicity with 'blocking'
Non monotonicity without 'blocking'
Monotonicity without 'blocking'
Computational analysis of first order moments evolution
Initial conditions of the system
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
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
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
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
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)
Evolution of the quantities F(t) (left) and G(t) (right)
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
 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
 [1] Daniel M. Romero, Christopher M. Kribs-Zaleta, Anuj Mubayi, Clara Orbe. An epidemiological approach to the spread of political third parties. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 707-738. doi: 10.3934/dcdsb.2011.15.707 [2] Evelyn K. Thomas, Katharine F. Gurski, Kathleen A. Hoffman. Analysis of SI models with multiple interacting populations using subpopulations. Mathematical Biosciences & Engineering, 2015, 12 (1) : 135-161. doi: 10.3934/mbe.2015.12.135 [3] Liling Lin, Linfeng Zhao. CCR model-based evaluation on the effectiveness and maturity of technological innovation. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1425-1437. doi: 10.3934/jimo.2021026 [4] Yang Liu, Zhiying Liu, Kaifei Xu. Imitative innovation or independent innovation strategic choice of emerging economies in non-cooperative innovation competition. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022023 [5] M. D. König, Stefano Battiston, M. Napoletano, F. Schweitzer. On algebraic graph theory and the dynamics of innovation networks. Networks and Heterogeneous Media, 2008, 3 (2) : 201-219. doi: 10.3934/nhm.2008.3.201 [6] Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci. Collisionless kinetic theory of rolling molecules. Kinetic and Related Models, 2013, 6 (2) : 429-458. doi: 10.3934/krm.2013.6.429 [7] Emmanuel Frénod, Mathieu Lutz. On the Geometrical Gyro-Kinetic theory. Kinetic and Related Models, 2014, 7 (4) : 621-659. doi: 10.3934/krm.2014.7.621 [8] Paolo Barbante, Aldo Frezzotti, Livio Gibelli. A kinetic theory description of liquid menisci at the microscale. Kinetic and Related Models, 2015, 8 (2) : 235-254. doi: 10.3934/krm.2015.8.235 [9] Hung-Wen Kuo. Effect of abrupt change of the wall temperature in the kinetic theory. Kinetic and Related Models, 2019, 12 (4) : 765-789. doi: 10.3934/krm.2019030 [10] José Antonio Alcántara, Simone Calogero. On a relativistic Fokker-Planck equation in kinetic theory. Kinetic and Related Models, 2011, 4 (2) : 401-426. doi: 10.3934/krm.2011.4.401 [11] Jingzhen Liu, Ka-Fai Cedric Yiu, Tak Kuen Siu, Wai-Ki Ching. Optimal insurance in a changing economy. Mathematical Control and Related Fields, 2014, 4 (2) : 187-202. doi: 10.3934/mcrf.2014.4.187 [12] Daewa Kim, Annalisa Quaini. A kinetic theory approach to model pedestrian dynamics in bounded domains with obstacles. Kinetic and Related Models, 2019, 12 (6) : 1273-1296. doi: 10.3934/krm.2019049 [13] José A. Carrillo, M. R. D’Orsogna, V. Panferov. Double milling in self-propelled swarms from kinetic theory. Kinetic and Related Models, 2009, 2 (2) : 363-378. doi: 10.3934/krm.2009.2.363 [14] Marzia Bisi, Tommaso Ruggeri, Giampiero Spiga. Dynamical pressure in a polyatomic gas: Interplay between kinetic theory and extended thermodynamics. Kinetic and Related Models, 2018, 11 (1) : 71-95. doi: 10.3934/krm.2018004 [15] Carlos Escudero, Fabricio Macià, Raúl Toral, Juan J. L. Velázquez. Kinetic theory and numerical simulations of two-species coagulation. Kinetic and Related Models, 2014, 7 (2) : 253-290. doi: 10.3934/krm.2014.7.253 [16] Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic and Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051 [17] M. Núñez-López, J. X. Velasco-Hernández, P. A. Marquet. The dynamics of technological change under constraints: Adopters and resources. Discrete and Continuous Dynamical Systems - B, 2014, 19 (10) : 3299-3317. doi: 10.3934/dcdsb.2014.19.3299 [18] Manuel Torrilhon. H-Theorem for nonlinear regularized 13-moment equations in kinetic gas theory. Kinetic and Related Models, 2012, 5 (1) : 185-201. doi: 10.3934/krm.2012.5.185 [19] Etienne Bernard, Laurent Desvillettes, Franç cois Golse, Valeria Ricci. A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures. Kinetic and Related Models, 2018, 11 (1) : 43-69. doi: 10.3934/krm.2018003 [20] Nicola Bellomo, Abdelghani Bellouquid, Juanjo Nieto, Juan Soler. Modeling chemotaxis from $L^2$--closure moments in kinetic theory of active particles. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 847-863. doi: 10.3934/dcdsb.2013.18.847

2020 Impact Factor: 1.432

## Metrics

• HTML views (51)
• Cited by (15)

## Other articlesby authors

• on AIMS
• on Google Scholar