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Complex Systems and Society pp 11–32Cite as

Mathematical Tools for Modeling Social Complex Systems

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Abstract

This chapter deals with the derivation of mathematical structures suitable for constructing models of phenomena of interest in social sciences. The reference framework is the approach of the Kinetic Theory for Active Particles (KTAP), which uses distribution functions over the microscopic states of the individuals composing the system under consideration. Modeling includes: the strategic behavior of active particles from a stochastic game perspective; a Darwinian-like evolution of the particles, which learn from past experience and evolve their strategy in time; and hints about small-network dynamics, in particular particle interactions within and among the nodes of the network. A critical analysis is finally proposed in order to assess the consistency of the mathematical tools with the main features of complexity.

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Authors and Affiliations

  1. Organization for Economic Co-Operation and Development, Paris, France

    Giulia Ajmone Marsan

  2. Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy

    Nicola Bellomo

  3. Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Rome, Italy

    Andrea Tosin

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Ajmone Marsan, G., Bellomo, N., Tosin, A. (2013). Mathematical Tools for Modeling Social Complex Systems. In: Complex Systems and Society. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7242-1_2

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