paper

Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory

arXiv:cond-mat/9805293 · doi:10.1016/0378-4371(93)90028-3

Abstract

In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is developed. Three kinds of social pair interactions are distinguished: Avoidance processes, compromising processes, and imitative processes. Computational results are presented for a special case of imitative processes: the competition of two equivalent strategies. They show a phase transition that describes the selforganization of a behavioral convention. This phase transition is further analyzed by examining the equations for the most probable behavioral distribution, which are Boltzmann-like equations. Special cases of Boltzmann-like equations do not obey the H-theorem and have oscillatory or even chaotic solutions. A suitable Taylor approximation leads to the socalled game dynamical equations (also known as selection-mutation equations in the theory of evolution).

For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html

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