Complex Systems and Society: Modeling and Simulation
Springer Science & Business Media, May 24, 2013 - Mathematics - 90 pages
This work aims to foster the interdisciplinary dialogue between mathematicians and socio-economic scientists. Interaction among scholars and practitioners traditionally coming from different research areas is necessary more than ever in order to better understand many real-world problems we face today. On the one hand, mathematicians need economists and social scientists to better address the methodologies they design in a more realistic way; on the other hand, economists and social scientists need to be aware of sound mathematical modelling tools in order to understand and, ultimately, solve the complex problems they encounter in their research. With this goal in mind, this work is designed to take into account a multidisciplinary approach that will encourage the transfer of knowledge, ideas, and methodology from one discipline to the other. In particular, the work has three main themes: Demystifying and unravelling complex systems; Introducing models of individual behaviours in the social and economic sciences; Modelling socio-economic sciences as complex living systems. Specific tools examined in the work include a recently developed modelling approach using stochastic game theory within the framework of statistical mechanics and progressing up to modeling Darwinian evolution. Special attention is also devoted to social network theory as a fundamental instrument for the understanding of socio-economic systems.
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Chapter 2 Mathematical Tools for Modeling Social Complex Systems
Chapter 3 Modeling Cooperation and Competition in SocioEconomic Systems
Applications and Simulations
Chapter 5 Forward Look at Research Perspectives
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active particles activity class activity variable analysis average U0 average wealth bounded rationality candidate particle chapter classes present Initial classes u1 collective behaviors complex systems complexity features cooperative and competitive corresponding mathematical critical threshold depends derivation of mathematical developed distribution function economic emerging behaviors Emerging bias evolution external actions field agents field particle functional subsystems game dynamics game theory Helbing initial conditions interaction dynamics interaction rate interplay kinetic theory KTAP approach living systems mathematical approaches mathematical models mathematical structures mathematical tools microscopic microscopic scale modeling approach monograph Multiscale networks node nonlinearly additive interactions numerical simulations open systems opinion formation ordinary differential equations outer environment parameter perspective phenomena population possible pre-interaction present Initial bias qualitative Sect social gap S0 social sciences social systems society socio-economic systems specific stochastic games studied table of games Tmax total number trends wealth classes wealth distribution wealth status welfare policy