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Nonlinear Maps and their Applications pp 69–88Cite as

Kinetic Exchange Models in Economics and Sociology

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 112))

Abstract

In this chapter, we briefly review the different aspects and applications of kinetic exchange models in economics and sociology. Our main aim is to show in what manner the kinetic exchange models for closed economic systems were inspired by the kinetic theory of gas molecules. The simple yet powerful framework of kinetic theory, first proposed in 1738, led to the successful development of statistical physics of gases towards the end of the nineteenth century. This framework was successfully adapted to modelling of wealth distributions in the early 2000s. In later times, it was applied to other areas like firm dynamics and opinion formation in the society, as well. We have tried to present the flavour of the several models proposed and their applications, intentionally leaving out the intricate mathematical and technical details.

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Notes

  1. 1.

    A classification of a variable generated by a statistical model that is explained by the relationships between functions within the model.

  2. 2.

    A variable whose value is determined outside the model in which it is used.

References

  1. Mandl, F.: Statistical Physics, 2nd edn. Wiley, New York (2002)

    Google Scholar 

  2. ter Haar, D.: Elements of Statistical Mechanics. Butterworth-Heinemann, Oxford (1995)

    Google Scholar 

  3. Sethna, J.P.: Statistical Mechanics. Oxford University Press, Oxford (2006)

    Google Scholar 

  4. Sinha, S., Chatterjee, A., Chakraborti, A., Chakrabarti, B.K.: Econophysics: An Introduction. Wiley-VCH, Berlin (2010)

    Google Scholar 

  5. Sen, P., Chakrabarti, B.K.: Sociophysics: An Introduction. Oxford University Press, Oxford (2013)

    Google Scholar 

  6. Ball, P.: Physica. A 314, 1 (2002)

    Google Scholar 

  7. Chakrabarti, B.K., Chakraborti, A., Chakravarty, S.R., Chatterjee, A.: Econophysics of Income and Wealth Distributions. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  8. Pareto, V.: Cours d’economie Politique. F. Rouge, Lausanne (1897)

    Google Scholar 

  9. Souma, W.: Growth and fluctuations of personal income. Fractals. 9, 463 (2001)

    Google Scholar 

  10. Di Matteo, T., Aste, T., Hyde, S.T.: In: Mallamace, F., Stanley, H.E. (eds.) The Physics of Complex Systems (New Advances and Perspectives), p. 43–5. IOS Press, Amsterdam (2004)

    Google Scholar 

  11. Clementi, F., Gallegati, M.: Power law tails in the Italian personal income distribution. Physica. A 350, 427 (2005)

    Google Scholar 

  12. Sinha, S.: Evidence for power-law tail of the wealth distribution in India. Physica. A 359, 555 (2006)

    Google Scholar 

  13. Silva, A.C., Yakovenko, V.M.: Temporal evolution of the “thermal” and “superthermal” income classes in the USA during 1983–2001. Europhys. Letts. 69, 304 (2005)

    Google Scholar 

  14. Drăgulescu, A.A., Yakovenko, V.M.: Statistical mechanics of money, income, and wealth: a short survey. Physica. A 299, 213 (2001)

    Google Scholar 

  15. Mandelbrot, B.B.: Fractional Brownian motions, fractional noises and applications. Int. Econ. Rev. 1, 79 (1960)

    Google Scholar 

  16. Chatterjee, A., Yarlagadda, S., Chakrabarti, B.K. (eds.): Econophysics of Wealth Distributions. Springer, Milan (2005)

    Google Scholar 

  17. Chakrabarti, B.K., Chakraborti, A., Chatterjee, A. (eds.): Econophysics and Sociophysics. Wiley-VCH, Berlin (2006)

    Google Scholar 

  18. Yakovenko, V.M., Barkley Rosser, J. Jr. Colloquium: statistical mechanics of money, wealth, and income. Rev. Mod. Phys. 81, 1703 (2009)

    Google Scholar 

  19. Drăgulescu, A.A., Yakovenko, V.M.: Evidence for the exponential distribution of income in the USA. Eur. Phys. J. B 20, 585 (2001)

    Google Scholar 

  20. Levy, M., Solomon, S.: New evidence for the power-law distribution of wealth. Physica. A 242, 90 (1997)

    Google Scholar 

  21. Aoyama, H., Souma, W., Fujiwara, Y.: Growth and fluctuations of personal and company’s income. Physica. A 324, 352 (2003)

    Google Scholar 

  22. Ding, N., Wang, Y.: Power-law tail in the Chinese wealth distribution. Chinese Phys. Letts. 24, 2434 (2007)

    Google Scholar 

  23. Chakrabarti, B.K., Marjit, S., Econophysics research in India in the last two decades. Ind. J. Phys. B 69, 681 (1995)

    Google Scholar 

  24. Ispolatov, S., Krapivsky, P.L., Redner, S.: Wealth distributions in asset exchange models. Eur. Phys. J. B 2, 267 (1998)

    Google Scholar 

  25. Drăgulescu, A.A., Yakovenko, V.M.: Statistical mechanics of money. Eur. Phys. J. B 17, 723 (2000)

    Google Scholar 

  26. Chakraborti, A., Chakrabarti, B.K.: Statistical mechanics of money: how saving propensity affects its distribution. Eur. Phys. J. B 17, 167 (2000)

    Google Scholar 

  27. Chatterjee, A., Chakrabarti, B.K.: Kinetic exchange models for income and wealth distributions. Eur. Phys. J. B 60, 135 (2007)

    Google Scholar 

  28. Chatterjee, A., Sinha, S., Chakrabarti, B.K.: Economic inequality: is it natural? Curr. Sci. 92, 1383 (2007)

    Google Scholar 

  29. Chakrabarti, A.S., Chakrabarti, B.K.: Statistical theories of income and wealth distribution. Economics E-journal 4 (2010) (http://www.economics-ejournal.org/economics/journalarticles/2010)

  30. Chatterjee, A.: In: Naldi, G., et al. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, p. 3–1. Birkhaüser, Boston (2010)

    Google Scholar 

  31. Chakraborti, A.: Distributions of money in model markets of economy. Int. J. Mod. Phys. C 13, 1315 (2002)

    Google Scholar 

  32. Hayes, B.: Follow the money. Am. Sci. 90, 400 (2002)

    Google Scholar 

  33. López-Ruiz, R., López, J.L., Calbet, X.: Complex systems with trivial dynamics. ESAIM Proc. 36, 189 (2012)

    Google Scholar 

  34. Patriarca, M., Chakraborti, A., Kaski, K.: Statistical model with a standard Gamma distribution. Phys. Rev. E 70, 016104 (2004)

    Google Scholar 

  35. Repetowicz, P., Hutzler, S., Richmond, P.: Dynamics of money and income distributions. Physica. A 356, 641 (2005)

    Google Scholar 

  36. Lallouache, M., Jedidi, A., Chakraborti, A.: Wealth distribution: to be or not to be a Gamma. Sci. Cul. 76, 478 (2010)

    Google Scholar 

  37. Angle, J.: The surplus theory of social stratification and the size distribution of personal wealth. Soc. Forc. 65, 293 (1986)

    Google Scholar 

  38. Angle, J.: The inequality process as a wealth maximizing process. Physica. A 367, 388 (2006)

    Google Scholar 

  39. Chakraborti, A., Patriarca, M.: Gamma-distribution and wealth inequality. Pramana J. Phys. 71, 233 (2008)

    Google Scholar 

  40. Chakraborti, A., Patriarca, M.: Variational principle for the pareto power law. Phys. Rev. Lett. 103, 228701 (2009)

    Google Scholar 

  41. Patriarca, M., Chakraborti, A.: Kinetic exchange models: from molecular physics to social science. Am. J. Phys. 81, 618 (2013)

    Google Scholar 

  42. Chatterjee, A., Chakrabarti, B.K., Manna, S.S.: Pareto law in a kinetic model of market with random saving propensity. Physica. A 335, 155 (2004)

    Google Scholar 

  43. Chatterjee, A., Chakrabarti, B.K., Manna, S.S.: Money in gas-like markets: Gibbs and Pareto Laws. Phys. Scr. T 106, 36 (2003)

    Google Scholar 

  44. Chatterjee, A., Chakrabarti, B.K., Stinchcombe, R.B.: Master equation for a kinetic model of a trading market and its analytic solution. Phys. Rev. E 72, 026126 (2005)

    Google Scholar 

  45. Mohanty, P.K.: Generic features of the wealth distribution in ideal-gas-like markets. Phys. Rev. E 74, 011117 (2006)

    Google Scholar 

  46. Kar Gupta, A.: In: Chakrabarti, B.K., Chakraborti, A., Chatterjee, A. (eds.) Econophysics and Sociophysics, p. 16–1. Wiley-VCH, Berlin (2006)

    Google Scholar 

  47. Chatterjee, A., Chakrabarti, B.K.: Ideal-gas-like market models with savings: quenched and annealed cases. Physica. A 382, 36 (2007)

    Google Scholar 

  48. Düring, B., Toscani, G.: Hydrodynamics from kinetic models of conservative economies. Physica. A 384, 493 (2007)

    Google Scholar 

  49. Düring, B., Matthes, D., Toscani, G.: Kinetic equations modelling wealth redistribution: a comparison of approaches. Phys. Rev. E 78, 056103 (2008)

    Google Scholar 

  50. Matthes, D., Toscani, G.: On steady distributions of kinetic models of conservative economies. J. Stat. Phys. 130, 1087 (2008)

    Google Scholar 

  51. Matthes, D., Toscani, G.: On steady distributions of kinetic models of conservative economies. Kinet. Relat. Models 1, 1 (2008)

    Google Scholar 

  52. Comincioli, V., Della Croce, L., Toscani, G.: A Boltzmann-like equation for choice formation. Kinet. Relat. Model. 2, 135 (2009)

    Google Scholar 

  53. Chatterjee, A.: Kinetic models for wealth exchange on directed networks. Eur. Phys.J. B 67, 593 (2009)

    Google Scholar 

  54. Chakrabarti, A.S., Chakrabarti, B.K.: Microeconomics of the ideal gas like market models. Physica. A 388, 4151 (2009)

    Google Scholar 

  55. Chakrabarti, A.S., Chakrabarti, B.K.: Inequality reversal: effects of the savings propensity and correlated returns. Physica. A 389, 3572 (2010)

    Google Scholar 

  56. Chakraborty, A., Manna, S.S.: Weighted trade network in a model of preferential bipartite transactions. Phys. Rev. E 81, 016111 (2010)

    Google Scholar 

  57. Iglesias, J.R.: How Simple Regulations can Greatly Reduce Inequality Science and Culture (Kolkata) 76, 437 (2010)

    Google Scholar 

  58. Pianegonda, S., Iglesias, J.R., Abramson, G., Vega, J.L.: Wealth redistribution with conservative exchanges Physica. A 322, 667 (2003)

    Google Scholar 

  59. Ghosh, A. (unpublished); Ghosh, A., Chakrabarti, A.S., Chandra, A.K., Chakraborti, A.: In: Abergel, F., Aoyama, H., Chakrabarti, B.K., Chakraborti, A., Ghosh, A. (eds.) Econophysics of Agent-Based Models, pp 99–129. Springer, Milan (2014)

    Google Scholar 

  60. Independent studies (unpublished) made by S. Sinha and also A. Chatterjee in 2005–2006, had similar observations; private communications

    Google Scholar 

  61. Ghosh, A., Basu, U., Chakraborti, A., Chakrabarti, B.K.: Threshold-induced phase transition in kinetic exchange models. Phys. Rev. E 83, 061130 (2011)

    Google Scholar 

  62. Chatterjee, A., Sen, P.: Agent dynamics in kinetic models of wealth exchange. Phys. Rev. E 82, 056117 (2010)

    Google Scholar 

  63. Goswami, S., Sen, P., Das, A.: Quantum persistence: a random-walk scenario. Phys. Rev. E 81, 021121 (2010)

    Google Scholar 

  64. Chakrabarti, A.S.: Bimodality in the firm size distributions: a kinetic exchange model approach. Eur. Phys. J. B 86, 255 (2013)

    Google Scholar 

  65. Chakrabarti, A.S.: Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models Physica. A 391, 6039 (2012)

    Google Scholar 

  66. Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591 (2009)

    Google Scholar 

  67. Galam, S.: Sociophysics: A Physicist’s Modeling of Psycho-Political Phenomena (Understanding Complex Systems). Springer, Heidelberg (2012)

    Google Scholar 

  68. Stauffer, D.: A biased review of sociophysics. J. Stat. Phys. 151, 9 (2013)

    Google Scholar 

  69. Lallouache, M., Chakraborti, A., Chakrabarti, B.K.: Kinetic exchange models for social opinion formation. Sci. Cult.76, 485 (2010)

    Google Scholar 

  70. Lallouache, M., Chakrabarti, A.S., Chakraborti, A., Chakrabarti, B.K.: Opinion formation in the kinetic exchange models: spontaneous symmetry breaking transition. Phys. Rev. E 82, 056112 (2010)

    Google Scholar 

  71. Biswas, S., Chandra, A.K., Chatterjee, A., Chakrabarti, B.K.: Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation. J. Phys. Conf. Ser. 297, 012004 (2011)

    Google Scholar 

  72. Sen, P.: Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges. Phys. Rev. E 83, 016108 (2011)

    Google Scholar 

  73. Biswas, S.: Mean-field solutions of kinetic-exchange opinion models. Phys. Rev. E 84, 056106 (2011)

    Google Scholar 

  74. Biswas, S., Chatterjee, A., Sen, P.: Disorder induced phase transition in kinetic models of opinion dynamics. Physica A 391, 3257 (2012)

    Google Scholar 

  75. Sen, P.: Nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence. Phys. Rev. E 84, 016115 (2012)

    Google Scholar 

  76. Chandra, A.K.: Percolation in a kinetic opinion exchange model. Phys. Rev. E 85, 021149 (2012)

    Google Scholar 

  77. Khaleque, A., Sen, P.: Damage spreading transition in an opinion dynamics model. Available at arXiv: 1312.7718v1 (2013)

    Google Scholar 

  78. Apenko, S.: Monotonic entropy growth for a nonlinear model of random exchanges. Phys. Rev. E 87, 024101 (2013)

    Google Scholar 

  79. López-Ruiz, R., Shivanian, E., López, J.L.: Random Market Models with an H-Theorem. Available at arXiv:1307.2169 (2013)

    Google Scholar 

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Acknowledgement

The authors would like to thank all their collaborators and students, whose works have been presented here.

Author information

Authors and Affiliations

  1. School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, 110067, India

    Anirban Chakraborti

  2. S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata, 700098, India

    Sanchari Goswami

Authors
  1. Sanchari Goswami
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  2. Anirban Chakraborti
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Corresponding author

Correspondence to Anirban Chakraborti .

Editor information

Editors and Affiliations

  1. Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, Spain

    Ricardo López-Ruiz

  2. Université de Toulouse, LAAS-CNRS, INSA, Toulouse, France

    Danièle Fournier-Prunaret

  3. Department of E.E. Eng., Tokushima University, Tokushima, Japan

    Yoshifumi Nishio

  4. Department of Mathematics, University of Évora, CIMA-UE, Évora, Portugal

    Clara Grácio

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Goswami, S., Chakraborti, A. (2015). Kinetic Exchange Models in Economics and Sociology. In: López-Ruiz, R., Fournier-Prunaret, D., Nishio, Y., Grácio, C. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-12328-8_4

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