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Explicit equilibria in bilinear kinetic models for socio-economic interactions. (English. French summary) Zbl 1335.91049

Summary: Bilinear kinetic models of Maxwell-Boltzmann type are often used to model socio-economic systems composed by agents that undergo binary interactions, which in general obey to some conservation law. Then, the details of the microscopic interaction are such that an equilibrium solution emerges. At difference with the classical Boltzmann equation for elastic gas particles, the analytic form of the equilibria is known only in some particular case. In the present note, we present and discuss the situations in which this equilibrium profile can be explicitly found. Applications to dissipative gases and to wealth redistribution models are presented.

MSC:

91B80 Applications of statistical and quantum mechanics to economics (econophysics)
82C40 Kinetic theory of gases in time-dependent statistical mechanics
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
35Q20 Boltzmann equations
35Q61 Maxwell equations
91B15 Welfare economics
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