Article:
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F. Rupp (2011): Modeling the Diffusion of Ideas by Stochastic Differential
Equations, HOMO OECONOMICUS, 28 (3), pp. 319-365.


Abstract:
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In recent times the concept of democracy has been widely discussed
due to civic revolts in the Arab world. As in biological settings,
the spread of ideas, rumors or inventions can be studied mathematically.
The aim of this paper is to present essential components of the underlying
model equations which incorporate random effects. First, ordinary
differential equation models are set up and extended to stochastic
differential equations for the diffusion of ideas. These are applied to
a multi-agent system that may shed some light on hidden social phenomena
(such as liberation movements in dictatorships) as well as the problem of
a simultaneous diffusion of two mutually exclusive ideas. We compare the
stochastic dynamics with the deterministic dynamics to show that proper
stochastic modeling reveals new insights compared to the known deterministic
setting.