The Role of Individual Behaviors in Socio-Economic Sciences

  • Giulia Ajmone Marsan
  • Nicola Bellomo
  • Andrea Tosin
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


This chapter provides an assessment of the relevant complexity features of social systems, focusing on the ability of individuals to express strategic behaviors that determine their interactions with other individuals. It also offers a concise survey of various modeling methods, which pertain to the cultural context of this monograph. Finally, this chapter critically assesses the effectiveness of the different mathematical approaches in capturing the complexity features of social systems.


Mathematical Tool Collective Behavior Behavioral Strategy Active Particle Mathematical Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Acemoglu, D., Bimpikis, K., Ozdaglar, A.: Dynamics of information exchange in endogenous social networks. Tech. Rep. 16410, National Bureau of Economic Research (2010)Google Scholar
  2. 2.
    Acemoglu, D., Robinson, J.A.: A theory of political transitions. American Economic Review 91(4), 938–963 (2001)CrossRefGoogle Scholar
  3. 3.
    Acemoglu, D., Robinson, J.A.: Economic Origins of Dictatorship and Democracy. Cambridge University Press (2006)Google Scholar
  4. 4.
    Agrawal, A., Cockburn, I., McHale, J.: Gone but not forgotten: knowledge flows, labor mobility, and enduring social relationships. Journal of Economic Geography 6(5), 571–591 (2006)CrossRefGoogle Scholar
  5. 5.
    Agrawal, A., Kapur, D., McHale, J.: How do spatial and social proximity influence knowledge flows? Evidence from patent data. Journal of Urban Economics 64(2), 258–269 (2008)CrossRefGoogle Scholar
  6. 6.
    Ajmone Marsan, G.: New paradigms towards the modelling of complex systems in Behavioral Economics. Mathematical and Computer Modelling 50(3–4), 584–597 (2009)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Ajmone Marsan, G.: On the modelling and simulation of the competition for a secession under media influence by active particles methods and functional subsystems decomposition. Computer & Mathematics with Applications 57(5), 710–728 (2009)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Ajmone Marsan, G., Bellomo, N., Egidi, M.: Towards a mathematical theory of complex socio-economical systems by functional subsystems representation. Kinetic and Related Models 1(2), 249–278 (2008)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Akerlof, G.A.: The market for “lemons”: Quality uncertainty and the market mechanism. Quarterly Journal of Economics 84(3), 488-500 (1970)CrossRefGoogle Scholar
  10. 10.
    Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Alesina, A., Baqir, R., Hoxby, C.: Political jurisdictions in heterogenous communities. Journal of Political Economy 112(2) (2004)Google Scholar
  12. 12.
    Aletti, G., Naldi, G., Toscani, G.: First-order continuous models of opinion formation. SIAM Journal on Applied Mathematics 67(3), 837–853 (2007)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Amaral, L.A.N., Scala, A., Barthélémy, M., Stanley, H.E.: Classes of small-world networks. Proceedings of the National Academy of Sciences 97(21), 11,149–11,152 (2000)Google Scholar
  14. 14.
    Antal, T., Traulsen, A., Ohtsuki, H., Tarnita, C.E., Nowak, M.A.: Mutation-selection equilibrium in games with multiple strategies. Journal of Theoretical Biology 258(4), 614–622 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ariel, R.: Modeling Bounded Rationality. MIT Press (1998)Google Scholar
  16. 16.
    Arlotti, L., Bellomo, N.: Solution of a new class of nonlinear kinetic models of population dynamics. Applied Mathematics Letters 9(2), 65–70 (1996)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Arlotti, L., Bellomo, N., De Angelis, E.: Generalized kinetic (Boltzmann) models: mathematical structures and applications. Mathematical Models and Methods in Applied Sciences 12(4), 567–591 (2002)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Arlotti, L., De Angelis, E.: On the initial value problem of a class of models of the kinetic theory for active particles. Applied Mathematics Letters 24(3), 257–263 (2011)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Arlotti, L., De Angelis, E., Fermo, L., Lachowicz, M., Bellomo, N.: On a class of integro-differential equations modeling complex systems with nonlinear interactions. Applied Mathematics Letters 25(3), 490–495 (2012)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Arthur, W.B., Durlauf, S.N., Lane, D.A. (eds.): The Economy as an Evolving Complex System II, Studies in the Sciences of Complexity, vol. XXVII. Addison-Wesley (1997)Google Scholar
  21. 21.
    Axelrod, R.M.: The complexity of cooperation: Agent-based models of competition and collaboration. Princeton University Press, Princeton (1997)Google Scholar
  22. 22.
    Azoulay, P., Zivin, J.S.G., Sampat, B.N.: The diffusion of scientific knowledge across time and space: Evidence from professional transitions for the superstars of medicine. Working Paper 16683, National Bureau of Economic Research (2011)Google Scholar
  23. 23.
    Bagarello, F., Oliveri, F.: A phenomenological operator description of interactions between populations with applications to migration. Mathematical Models and Methods in Applied Sciences 23(3), 471–492 (2013)MATHCrossRefGoogle Scholar
  24. 24.
    Ball, P.: Why Society is a Complex Matter. Springer-Verlag, Heidelberg (2012)CrossRefGoogle Scholar
  25. 25.
    Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Parisi, G., Procaccini, A., Viale, M., Zdravkovic, V.: Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study. Proceedings of the National Academy of Sciences 105(4), 1232–1237 (2008)CrossRefGoogle Scholar
  26. 26.
    Banasiak, J., Lachowicz, M.: Multiscale approach in mathematical biology. Comment on “Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives” by N. Bellomo and B. Carbonaro. Physics of Life Reviews 8, 19–20 (2011)CrossRefGoogle Scholar
  27. 27.
    Barabási, A.L.: The Science of Networks. Perseus, Cambridge MA (2022)Google Scholar
  28. 28.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Barabási, A.L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A 272(1), 173–187 (1999)CrossRefGoogle Scholar
  30. 30.
    Barbera, S., Maschler, M., Shalev, J.: Voting for voters: A model of electoral evolution. Games and Economic Behavior 37(1), 40–78 (2001)MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Barca, F.: An Agenda for a Reformed Cohesion Policy: A place-based approach to meeting European Union challenges and expectations. EERI Research Paper Series EERI_RP_2008_06, Economics and Econometrics Research Institute (EERI), Brussels (2008)Google Scholar
  32. 32.
    Barrat, A., Bathélemy, M., Vespignani, A.: The Structure and Dynamics of Networks. Princeton University Press, Princeton NJ (2006)Google Scholar
  33. 33.
    Bastolla, U., Fortuna, M.A., Pascual-García, A., Ferrera, A., Luque, B., Bascompte, J.: The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458, 1018–1020 (2009)CrossRefGoogle Scholar
  34. 34.
    Bellomo, N.: Modeling Complex Living Systems: A Kinetic Theory and Stochastic Game Approach. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (2007)Google Scholar
  35. 35.
    Bellomo, N.: Modeling the hiding-learning dynamics in large living systems. Applied Mathematics Letters 23(8), 907–911 (2010)MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    Bellomo, N., Bellouquid, A., Nieto, J., Soler, J.: On the asymptotic theory from microscopic to macroscopic growing tissue models: An overview with perspectives. Mathematical Models and Methods in Applied Sciences 22(1), 1130,001 (37 pages) (2012)Google Scholar
  37. 37.
    Bellomo, N., Berestycki, H., Brezzi, F., Nadal, J.P.: Mathematics and complexity in life and human sciences. Mathematical Models and Methods in Applied Sciences 19(supp01), 1385–1389 (2009)Google Scholar
  38. 38.
    Bellomo, N., Coscia, V.: Sources of nonlinearity in the kinetic theory of active particles with focus on the formation of political opinions. In: E. Mitidieri, V.D. Radulescu, J. Serrin (eds.) Proceedings of the Conference on Nonlinear Partial Differential Equations, Contemporary Mathematics Series of the American Mathematical Society. American Mathematical Society, Philadelphia (2013)Google Scholar
  39. 39.
    Bellomo, N., Herrero, M.A., Tosin, A.: On the dynamics of social conflicts looking for the Black Swan. Kinetic and Related Models 6(3), (2013)Google Scholar
  40. 40.
    Bellomo, N., Knopoff, D., Soler, J.: On the difficult interplay between life, “complexity”, and mathematical sciences. Mathematical Models and Methods in Applied Sciences 23, (2013)Google Scholar
  41. 41.
    Bellomo, N., Lods, B., Revelli, R., Ridolfi, L.: Generalized collocation methods: Solutions to nonlinear problems. Modeling and Simulation In Science, Engineering and Technology. Birkhäuser, Boston (2007)Google Scholar
  42. 42.
    Bellomo, N., Piccoli, B., Tosin, A.: Modeling crowd dynamics from a complex system viewpoint. Mathematical Models and Methods in Applied Sciences 22, 1230,004 (29 pages) (2012)Google Scholar
  43. 43.
    Bellomo, N., Soler, J.: On the mathematical theory of the dynamics of swarms viewed as complex systems. Mathematical Models and Methods in Applied Sciences 22(supp01), 1140,006 (29 pages) (2012)Google Scholar
  44. 44.
    Bellouquid, A., Delitala, M.: Mathematical modeling of complex biological systems: A kinetic theory approach. Modeling and Simulation In Science, Engineering and Technology. Birkhäuser, Boston (2006)Google Scholar
  45. 45.
    Berinsky, A.J., Burns, N., Traugott, M.W.: Who votes by mail?: A dynamic model of the individual-level consequences of voting-by-mail systems. Public Opinion Quarterly 65(2), 178–197 (2001)CrossRefGoogle Scholar
  46. 46.
    Bertotti, M.L.: Modelling taxation and redistribution: A discrete active particle kinetic approach. Applied Mathematics and Computation 217(2), 752–762 (2010)MathSciNetMATHCrossRefGoogle Scholar
  47. 47.
    Bertotti, M.L.: On a class of dynamical systems with emerging cluster structure. Journal of Differential Equations 249(11), 2757–2770 (2010)MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    Bertotti, M.L., Delitala, M.: From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences. Mathematical Models and Methods in Applied Sciences 14(7), 1061–1084 (2004)MathSciNetMATHCrossRefGoogle Scholar
  49. 49.
    Bertotti, M.L., Delitala, M.: Conservation laws and asymptotic behavior of a model of social dynamics. Nonlinear Analysis: Real World Applications 9(1), 183–196 (2008)MathSciNetMATHCrossRefGoogle Scholar
  50. 50.
    Bertotti, M.L., Delitala, M.: On a discrete generalized kinetic approach for modelling persuader’s influence in opinion formation processes. Mathematical and Computer Modelling 48(7), 1107–1121 (2008)MathSciNetMATHCrossRefGoogle Scholar
  51. 51.
    Bertotti, M.L., Delitala, M.: On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders. Mathematical Models and Methods in Applied Sciences 18(6), 913–934 (2008)MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    Bertotti, M.L., Delitala, M.: Cluster formation in opinion dynamics: a qualitative analysis. Zeitschrift für angewandte Mathematik und Physik 61(4), 583–602 (2010)MathSciNetMATHCrossRefGoogle Scholar
  53. 53.
    Bertotti, M.L., Modanese, G.: From microscopic taxation and redistribution models to macroscopic income distributions. Physica A 390(21–22), 3782–3793 (2011)CrossRefGoogle Scholar
  54. 54.
    Bettencourt, L., Lobo, J., Helbing, D., Kühnert, C., West, G.B.: Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences 104(17), 7301 (2007)CrossRefGoogle Scholar
  55. 55.
    Bisi, M., Spiga, G., Toscani, G.: Kinetic models of conservative economies with wealth redistribution. Communications in Mathematical Sciences 7(4), 901–916 (2009)MathSciNetMATHGoogle Scholar
  56. 56.
    Borjas, G.J.: Economic theory and international migration. International Migration Review 23(3), 457–485 (1989)CrossRefGoogle Scholar
  57. 57.
    Bressan, A.: Bifurcation analysis of a non-cooperative differential game with one weak player. Journal of Differential Equations 248(6), 1297–1314 (2010)MathSciNetMATHCrossRefGoogle Scholar
  58. 58.
    Bressan, A.: Noncooperative differential games. A tutorial (2010). URL Lecture Notes for a Summer Course
  59. 59.
    Bressan, A., Shen, W.: Semi-cooperative strategies for differential games. International Journal of Game Theory 32(4), 561–593 (2004)MathSciNetMATHCrossRefGoogle Scholar
  60. 60.
    Bursik, R.J.: Social disorganization and theories of crime and delinquency: Problems and prospects. Criminology 26(4), 519–551 (1988)CrossRefGoogle Scholar
  61. 61.
    Camilli, F., Capuzzo Dolcetta, I., Falcone, M.: Preface. Networks and Heterogeneous Media 7(2), i–ii (2012). Special Issue on Mean Field GamesGoogle Scholar
  62. 62.
    Cavagna, A., Cimarelli, A., Giardina, I., Parisi, G., Santagati, R., Stefanini, F., Tavarone, R.: From empirical data to inter-individual interactions: Unveiling the rules of collective animal behavior. Mathematical Models and Methods in Applied Sciences 20(supp01), 1491–1510 (2010)Google Scholar
  63. 63.
    Cebula, R.J., Vedder, R.K.: A note on migration, economic opportunity, and the quality of life. Journal of Regional Science 13(2), 205–211 (1973)CrossRefGoogle Scholar
  64. 64.
    Cohen, W.M., Levinthal, D.A.: Absorptive capacity: a new perspective on learning and innovation. Administrative Science Quarterly 35(1), 128–152 (1990)CrossRefGoogle Scholar
  65. 65.
    Comincioli, V., Della Croce, L., Toscani, G.: A Boltzmann-like equation for choice formation. Kinetic and Related Models 2(1), 135–149 (2009)MathSciNetMATHCrossRefGoogle Scholar
  66. 66.
    Coscia, V., Fermo, L., Bellomo, N.: On the mathematical theory of living systems II: The interplay between mathematics and system biology. Computers & Mathematics with Applications 62(10), 3902–3911 (2011)MathSciNetMATHCrossRefGoogle Scholar
  67. 67.
    Cowan, R., Jonard, N.: Network structure and the diffusion of knowledge. Journal of Economic Dynamics and Control 28(8), 1557–1575 (2004)MathSciNetMATHCrossRefGoogle Scholar
  68. 68.
    Crescenzi, R., Rodriguez-Pose, A.: Innovation and Regional Growth in the European Union. Springer, Berlin, Heidelberg (2011)CrossRefGoogle Scholar
  69. 69.
    Cristiani, E., Piccoli, B., Tosin, A.: Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Modeling & Simulation 9(1), 155–182 (2011)MathSciNetMATHCrossRefGoogle Scholar
  70. 70.
    Cristiani, E., Piccoli, B., Tosin, A.: How can macroscopic models reveal self-organization in traffic flow? In: Proceedings of the 51st IEEE Conference on Decision and Control (2012)Google Scholar
  71. 71.
    Cushing, B., Poot, J.: Crossing boundaries and borders: Regional science advances in migration modelling. Papers in Regional Science 83(1), 317–338 (2004)Google Scholar
  72. 72.
    De Lillo, S., Bellomo, N.: On the modeling of collective learning dynamics. Applied Mathematics Letters 24(11), 1861–1866 (2011)MathSciNetMATHCrossRefGoogle Scholar
  73. 73.
    De Lillo, S., Delitala, M., Salvatori, C.: Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles. Mathematical Models and Methods in Applied Sciences 19(1), 1405–1425 (2009)MathSciNetMATHCrossRefGoogle Scholar
  74. 74.
    De Montis, A., Barthélemy, M., Chessa, A., Vespignani, A.: The structure of inter-urban traffic: A weighted network analysis. Environment and Planning B 34, 905–924 (2007)CrossRefGoogle Scholar
  75. 75.
    Deutsch, A., Dormann, S.: Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (2005)MATHGoogle Scholar
  76. 76.
    Dobson, D., St. Angelo, D.: Party identification and the floating vote: some dynamics. The American Political Science Review 69(2), 481–490 (1975)Google Scholar
  77. 77.
    Dreber, A., Nowak, M.A.: Gambling for global goods. Proceedings of the National Academy of Sciences 105(7), 2261 (2008)CrossRefGoogle Scholar
  78. 78.
    Düring, B., Markowich, P., Pietschmann, J.F., Wolfram, M.T.: Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proceedings of the Royal Society A 465(2112), 3687–3708 (2009)MATHCrossRefGoogle Scholar
  79. 79.
    Dyer, J.R.G., Johansson, A., Helbing, D., Couzin, I., Krause, J.: Leadership, consensus decision making and collective behaviour in humans. Philosophical Transactions of the Royal Society B: Biological Sciences 364(1518), 781–789 (2009)CrossRefGoogle Scholar
  80. 80.
    Dyson, J., Villella-Bressan, R., Webb, G.F.: The steady state of a maturity structured tumor cord cell population. Discrete and Continous Dynamical Systems B 4(1), 115–134 (2004)MathSciNetMATHGoogle Scholar
  81. 81.
    Ehrhardt, G.C.M.A., Marsili, M., Vega-Redondo, F.: Phenomenological models of socioeconomic network dynamics. Physical Review E 74(3), 036,106 (2006)MathSciNetCrossRefGoogle Scholar
  82. 82.
    Epstein, J.M., Axtell, R.: Growing Artificial Societies: Social Science from the Bottom Up. The MIT Press (1996)Google Scholar
  83. 83.
    Fudenberg, D., Nowak, M.A., Taylor, C., Imhof, L.A.: Evolutionary game dynamics in finite populations with strong selection and weak mutation. Theoretical Population Biology 70(3), 352–363 (2006)MATHCrossRefGoogle Scholar
  84. 84.
    Galam, S.: Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate. Physica A 390(17), 3036–3054 (2011)CrossRefGoogle Scholar
  85. 85.
    Gauvin, L., Vannimenus, J., Nadal, J.P.: Phase diagram of a Schelling segregation model. The European Physical Journal B 70(2), 293–304 (2009)CrossRefGoogle Scholar
  86. 86.
    Gerber, A., Karlan, D.S., Bergan, D.: Does the media matter? A field experiment measuring the effect of newspapers on voting behavior and political opinions. Discussion paper 12, Yale University, Department of Economics (2006). Yale Working Papers on Economic Applications and PolicyGoogle Scholar
  87. 87.
    Gintis, H.: Beyond Homo Economicus: evidence from experimental economics. Ecological Economics 35(3), 311–322 (2000)CrossRefGoogle Scholar
  88. 88.
    Gintis, H.: Game theory evolving: A problem-centered introduction to modeling strategic behavior. Princeton University Press (2000)Google Scholar
  89. 89.
    Goyal, S.: Connections: An introduction to the economics of networks. Princeton University Press (2009)Google Scholar
  90. 90.
    Goyal, S., Vega-Redondo, F.: Network formation and social coordination. Games and Economic Behavior 50(2), 178–207 (2005)MathSciNetMATHCrossRefGoogle Scholar
  91. 91.
    Granovetter, M.S.: The strength of weak ties. American Journal of Sociology 78(6), 1360–1380 (1973)CrossRefGoogle Scholar
  92. 92.
    Guéant, O., Lasry, J., Lions, P.: Mean field games and applications. In: Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Mathematics, vol. 2003, pp. 205–266. Springer, Berlin, Heidelberg (2011)Google Scholar
  93. 93.
    Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402(supp), C47–C52 (1999)Google Scholar
  94. 94.
    Helbing, D.: Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory. Physica A 193(2), 241–258 (1993)MathSciNetCrossRefGoogle Scholar
  95. 95.
    Helbing, D.: Quantitative sociodynamics: Stochastic methods and models of social interaction processes. Springer Verlag (2010)Google Scholar
  96. 96.
    Helbing, D.: New ways to promote sustainability and social well-being in a complex, strongly interdependent world: The futurist approach. In: P. Ball (ed.) Why Society is a Complex Matter, Lecture Notes in Mathematics, pp. 55–60. Springer, Berlin Heidelberg (2012)CrossRefGoogle Scholar
  97. 97.
    Helbing, D.: Social Self-Organization. Springer-Verlag, Berlin (2012)CrossRefGoogle Scholar
  98. 98.
    Helbing, D., Johansson, A.: Pedestrian, crowd, and evacuation dynamics. In: R.A. Meyers (ed.) Encyclopedia of Complexity and Systems Science, vol. 16, pp. 6476–6495. Springer, New York (2009)CrossRefGoogle Scholar
  99. 99.
    Helbing, D., Sigmeier, J., Lämmer, S.: Self-organized network flows. Networks and Heterogeneous Media 2(2), 193–210 (2007)MathSciNetMATHCrossRefGoogle Scholar
  100. 100.
    Helbing, D., Szolnoki, A., Perc, M., Szabó, G.: Defector-accelerated cooperativeness and punishment in public goods games with mutations. Physical Review E 81(5), 057,104 (2010)Google Scholar
  101. 101.
    Helbing, D., Yu, W.: The outbreak of cooperation among success-driven individuals under noisy conditions. Proceedings of the National Academy of Sciences 106(10), 3680–3685 (2009)CrossRefGoogle Scholar
  102. 102.
    Helbing, D., Yu, W.: The future of social experimenting. Proceedings of the National Academy of Sciences 107(12), 5265–5266 (2010)CrossRefGoogle Scholar
  103. 103.
    Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H., McElreath, R.: In search of homo economicus: behavioral experiments in 15 small-scale societies. The American Economic Review 91(2), 73–78 (2001)CrossRefGoogle Scholar
  104. 104.
    Herbert, S.: A behavioral model of rational choice. In: Models of Man, Social and Rational: Mathematical Essays on Rational Human Behavior in a Social Setting. Wiley, New York (1957)Google Scholar
  105. 105.
    Herbert, S.: Bounded rationality and organizational learning. Organization Science 2(1), 125–134 (1991)MathSciNetCrossRefGoogle Scholar
  106. 106.
    Herrero, M.A.: Through a glass, darkly: biology seen from mathematics: comment on “Toward a mathematical theory of living systems focusing on developmental biology and evolution: a review and perspectives” by N. Bellomo and B. Carbonaro. Physics of Life Reviews 8(1), 21 (2011)CrossRefGoogle Scholar
  107. 107.
    Jensen, M.B., Johnson, B., Lorenz, E., Lundvall, B.Å.: Forms of knowledge and modes of innovation. Research Policy 36(5), 680–693 (2007)CrossRefGoogle Scholar
  108. 108.
    Kirman, A.: Complex Economics: Individual and collective rationality. Routledge, London (2011)Google Scholar
  109. 109.
    Kirman, A.P., Vriend, N.J.: Learning to be loyal. A study of the Marseille fish market, Lecture Notes in Economics and Mathematical Systems, vol. 484. Springer (2000)Google Scholar
  110. 110.
    Kirman, A.P., Zimmermann, J.B.: Economics with Heterogeneous Interacting Agents. No. 503 in Lecture Notes in Economics and Mathematical Systems. Springer, Berlin Heidelberg (2001)Google Scholar
  111. 111.
    Knopoff, D.: On the modeling of migration phenomena on small networks. Mathematical Models and Methods in Applied Sciences 23(3), 541–563 (2012)CrossRefGoogle Scholar
  112. 112.
    Lachowicz, M.: Individually-based Markov processes modeling nonlinear systems in mathematical biology. Nonlinear Analysis: Real World Applications 12(4), 2396–2407 (2011)MathSciNetMATHCrossRefGoogle Scholar
  113. 113.
    Langer, P., Nowak, M.A., Hauert, C.: Spatial invasion of cooperation. Journal of Theoretical Biology 250(4), 634–641 (2008)MathSciNetCrossRefGoogle Scholar
  114. 114.
    Lasry, J.M., Lions, P.L.: Mean field games. Japanese Journal of Mathematics 2(1), 229–260 (2007)MathSciNetMATHCrossRefGoogle Scholar
  115. 115.
    Lipsey, R.G., Lancaster, K.: The general theory of second best. The Review of Economic Studies 24(1), 11–32 (1956)CrossRefGoogle Scholar
  116. 116.
    Maldarella, D., Pareschi, L.: Kinetic models for socio-economic dynamics of speculative markets. Physica A 391(3), 715–730 (2012)CrossRefGoogle Scholar
  117. 117.
    Markus, G.B., Converse, P.E.: A dynamic simultaneous equation model of electoral choice. The American Political Science Review 73(4), 1055–1070 (1979)CrossRefGoogle Scholar
  118. 118.
    Marvel, S.A., Kleinberg, J., Kleinberg, R.D., Strogatz, S.H.: Continuous-time model of structural balance. Proceedings of the National Academy of Sciences 108(5), 1771–1776 (2011)CrossRefGoogle Scholar
  119. 119.
    May, R.M.: Uses and abuses of Mathematics in Biology. Science 303(5659), 790–793 (2004)CrossRefGoogle Scholar
  120. 120.
    Mayr, E.: The philosophical foundations of Darwinism. Proceedings of the American Philosphical Society 145(4), 488–495 (2001)Google Scholar
  121. 121.
    Milgram, S.: The small world problem. Psychology Today 2(1), 60–67 (1967)MathSciNetGoogle Scholar
  122. 122.
    Morgenstern, O., Von Neumann, J.: Theory of games and economic behavior. Princeton University Press (1953)Google Scholar
  123. 123.
    Nowak, M.A.: Evolutionary Dynamics. Exploring the Equations of Life. Harvard University Press (2006)MATHGoogle Scholar
  124. 124.
    Nowak, M.A.: Five rules for the evolution of cooperation. Science 314(5805), 1560–1563 (2006)CrossRefGoogle Scholar
  125. 125.
    Nowak, M.A., Ohtsuki, H.: Prevolutionary dynamics and the origin of evolution. Proceedings of the National Academy of Sciences 105(39), 14,924–14,927 (2008)Google Scholar
  126. 126.
    Nowak, M.A., Sigmund, K.: Evolutionary dynamics of biological games. Science 303(5659), 793–799 (2004)CrossRefGoogle Scholar
  127. 127.
    Nuño, J.C., Herrero, M.A., Primicerio, M.: A mathematical model of a criminal-prone society. Discrete and Continuous Dynamical Systems - Series S 4(1), 193–207 (2011)MathSciNetMATHCrossRefGoogle Scholar
  128. 128.
    OECD: Divided We Stand: Why Inequality Keeps Rising. OECD Publishing (2011)Google Scholar
  129. 129.
    OECD: Regional Outlook, Building Resilient Regions for Stronger Economies. OECD Publishing (2011)Google Scholar
  130. 130.
    Ohtsuki, H., Pacheco, J.M., Nowak, M.A.: Evolutionary graph theory: Breaking the symmetry between interaction and replacement. Journal of Theoretical Biology 246(4), 681–694 (2007)MathSciNetCrossRefGoogle Scholar
  131. 131.
    Olson, M.: Dictatorship, democracy, and development. American Political Science Review 87(3), 567–576 (1993)CrossRefGoogle Scholar
  132. 132.
    Osborne, M.J., Rubinstein, A.: A course in game theory. The MIT press (1994)Google Scholar
  133. 133.
    Perthame, B.: Transport Equations in Biology. Birkhäuser (2007)Google Scholar
  134. 134.
    Piccoli, B., Tosin, A.: Pedestrian flows in bounded domains with obstacles. Continuum Mechanics and Thermodynamics 21(2), 85–107 (2009)MathSciNetMATHCrossRefGoogle Scholar
  135. 135.
    Piff, P.K., Stancato, D.M., Côté, S., Mendoza-Denton, R., Keltner, D.: Higher social class predicts increased unethical behavior. Proceedings of the National Academy of Sciences 109(11), 4086–4091 (2012)Google Scholar
  136. 136.
    Rand, D.G., Arbesman, S., Christakis, N.A.: Dynamic social networks promote cooperation in experiments with humans. Proceedings of the National Academy of Sciences 108(48), 19,193–19,198 (2011)Google Scholar
  137. 137.
    Sah, R.K.: Social osmosis and patterns of crime. Journal of Political Economy 99(6), 1272–1295 (1991)CrossRefGoogle Scholar
  138. 138.
    Santos, F.C., Pacheco, J.M., Lenaerts, T.: Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proceedings of the National Academy of Sciences 103(9), 3490–3494 (2006)CrossRefGoogle Scholar
  139. 139.
    Santos, F.C., Vasconcelos, V., Santos, M.D., Neves, P., Pacheco, J.M.: Evolutionary dynamics of climate change under collective-risk dilemmas. Mathematical Models and Methods in Applied Sciences 22, 1140,004 (17 pages) (2012)Google Scholar
  140. 140.
    Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., van Nes, E.H., Rietkerk, M., Sugihara, G.: Early-warning signals for critical transitions. Nature 461, 53–59 (2009)CrossRefGoogle Scholar
  141. 141.
    Schrödinger, E.: What is Life? The Physical Aspect of the Living Cell. Cambridge University Press, Cambridge (1944)Google Scholar
  142. 142.
    Short, M.B., Brantingham, P.J., Bertozzi, A.L., Tita, G.E.: Dissipation and displacement of hotspots in reaction-diffusion models of crime. Proceedings of the National Academy of Sciences 107(9), 3961–3965 (2010)CrossRefGoogle Scholar
  143. 143.
    Short, M.B., D’Orsogna, M.R., Pasour, V.B., Tita, G.E., Brantingham, P.J., Bertozzi, A.L., Chayes, L.B.: A statistical model of criminal behavior. Mathematical Models and Methods in Applied Sciences 18(S1), 1249–1267 (2008)MathSciNetMATHCrossRefGoogle Scholar
  144. 144.
    Sigmund, K.: The Calculus of Selfishness. Princeton University Series in Theoretical and Computational Biology, Princeton, USA (2011)Google Scholar
  145. 145.
    Simon, H.A.: Theories of decision-making in Economics and Behavioral Science. The American Economic Review 49(3), 253–283 (1959)Google Scholar
  146. 146.
    Spolaore, E.: Civil conflict and secessions. Economics of Governance 9(1), 45–63 (2009)CrossRefGoogle Scholar
  147. 147.
    Stiglitz, J.E.: Information and the change in the paradigm in economics. The American Economic Review 92(3), 460–501 (2009)CrossRefGoogle Scholar
  148. 148.
    Strogatz, S.H.: Exploring complex networks. Nature 410(6825), 268–276 (2001)CrossRefGoogle Scholar
  149. 149.
    Taleb, N.N.: The Black Swan: The Impact of the Highly Improbable. Random House, New York City (2007)Google Scholar
  150. 150.
    Taleb, N.N.: Force et fragilité. Réflexions philosophiques et empiriques. Les Belles Lettres, Paris (2010)Google Scholar
  151. 151.
    Thaler, R.H.: From Homo Economicus to Homo Sapiens. The Journal of Economic Perspectives 14(1), 133–141 (2000)CrossRefGoogle Scholar
  152. 152.
    Toscani, G.: Kinetic models of opinion formation. Communications in Mathematical Sciences 4(3), 481–496 (2006)MathSciNetMATHGoogle Scholar
  153. 153.
    Traulsen, A., Hauert, C., De Silva, H., Nowak, M.A., Sigmund, K.: Exploration dynamics in evolutionary games. Proceedings of the National Academy of Sciences 106(3), 709–712 (2009)MATHCrossRefGoogle Scholar
  154. 154.
    Traulsen, A., Iwasa, Y., Nowak, M.A.: The fastest evolutionary trajectory. Journal of Theoretical Biology 249(3), 617–623 (2007)MathSciNetCrossRefGoogle Scholar
  155. 155.
    Traulsen, A., Pacheco, J.M., Nowak, M.A.: Pairwise comparison and selection temperature in evolutionary game dynamics. Journal of Theoretical Biology 246(3), 522–529 (2007)MathSciNetCrossRefGoogle Scholar
  156. 156.
    Turchin, P.: Complex population dynamics: a theoretical/empirical synthesis, vol. 35. Princeton University Press (2003)Google Scholar
  157. 157.
    Van Kempen, E.T.: The dual city and the poor: social polarisation, social segregation and life chances. Urban Studies 31(7), 995 (1994)CrossRefGoogle Scholar
  158. 158.
    Vega-Redondo, F.: Complex social networks, vol. 44. Cambridge University Press (2007)Google Scholar
  159. 159.
    Von Hippel, E.: “Sticky information” and the locus of problem solving: Implications for innovation. Management Science 40(4), 429–439 (1994)CrossRefGoogle Scholar
  160. 160.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)CrossRefGoogle Scholar
  161. 161.
    Webb, G.F.: Theory of Nonlinear Age-dependent Population Dynamics. Dekker, New York (1985)MATHGoogle Scholar
  162. 162.
    Weidlich, W.: Sociodynamics: A Systematic Approach to Modeling the Social Sciences. Harwood, Academic, Amsterdam (2002)Google Scholar
  163. 163.
    Wood, A.J., Ackland, G.J., Dyke, J.G., Williams, H.T.P., Lenton, T.M.: Daisyworld: A review. Reviews of Geophysics 46(1), RG1001 (23 pages) (2008)Google Scholar
  164. 164.
    Yu, W., Helbing, D.: Game theoretical interactions of moving agents. In: Simulating Complex Systems by Cellular Automata, Understanding Complex Systems, Chapter 10, pp. 219–239. Springer, Berlin Heidelberg (2010)Google Scholar
  165. 165.
    Zhao, Z., Kirou, A., Ruszczycki, B., Johnson, N.F.: Dynamical clustering as a generator of complex system dynamics. Mathematical Models and Methods in Applied Sciences 19(supp01), 1539–1566 (2009)Google Scholar

Copyright information

© Nicola Bellomo, Giulia Ajmone, Andrea Tosin 2013

Authors and Affiliations

  • Giulia Ajmone Marsan
    • 1
  • Nicola Bellomo
    • 2
  • Andrea Tosin
    • 3
  1. 1.Organization for Economic Co-Operation and DevelopmentParisFrance
  2. 2.Department of Mathematical SciencesPolitecnico di TorinoTorinoItaly
  3. 3.Istituto per le Applicazioni del Calcolo “M. Picone”Consiglio Nazionale delle RicercheRomeItaly

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