Kinetic modelling of multiple interactions in socio-economic systems

Giuseppe Toscani; Andrea Tosin; Mattia Zanella; Giuseppe Toscani; Andrea Tosin; Mattia Zanella

doi:10.3934/nhm.2020029

Networks and Heterogeneous Media

2020, Volume 15, Issue 3: 519-542. doi: 10.3934/nhm.2020029

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Kinetic modelling of multiple interactions in socio-economic systems

1.
Department of Mathematics "F. Casorati", University of Pavia, Via A. Ferrata 5, 27100 Pavia, Italy
2.
Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

Received: 01 October 2019 Revised: 01 March 2020 Published: 09 September 2020
Primary: 35Q20; Secondary: 35Q84, 82B21, 91D10

Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider, in various situations, multiple interactions among the individuals. In this paper, we collect and discuss some examples related to economic and gambling activities. In particular, we focus on a linearisation strategy of the multiple interactions, which greatly simplifies the kinetic description of such systems while maintaining all their essential aggregate features, including the equilibrium distributions.
- Multiple-collision Boltzmann equation,
- linearised kinetic models,
- Fokker-Planck equation
Citation: Giuseppe Toscani, Andrea Tosin, Mattia Zanella. Kinetic modelling of multiple interactions in socio-economic systems[J]. Networks and Heterogeneous Media, 2020, 15(3): 519-542. doi: 10.3934/nhm.2020029

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Abstract

Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider, in various situations, multiple interactions among the individuals. In this paper, we collect and discuss some examples related to economic and gambling activities. In particular, we focus on a linearisation strategy of the multiple interactions, which greatly simplifies the kinetic description of such systems while maintaining all their essential aggregate features, including the equilibrium distributions.

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