Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory
✍ Scribed by Dirk Helbing
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 687 KB
- Volume
- 193
- Category
- Article
- ISSN
- 0378-4371
No coin nor oath required. For personal study only.
✦ Synopsis
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 self-organization of a behavioral convention. This phase transition is further analyzed by examining the equations for the most probable behavioral distribution, which are Boltzmannlike 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 so-called game dynamical equations (also known as selection-mutation equations in the theory of evolution).