Generalized Polya urn model with tness and non-linear reinforcement
F.M. Jacobs (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Stefan Grosskinsky – Mentor (TU Delft - Applied Probability)
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Abstract
In this report a generalized Polya urn model is considered where there is nonlinear reinforcement and each component has a tness. The transition probability is proportional to feedback functions of the model and thus depends on the component that is considered. Models with these feedback functions can reach a monopoly or dierent stable state after a nite amount of time. The kind of stable state that is reached depends on the value of the non-linear reinforcement and the exact form of the stable state depends on the tness and initial conditions of the components. In this report the behavior of the model is illustrated using ow elds in the cases of k = 2 and k = 3. It is also proven when monopoly is reached for a particular feedback function and that the simplex for this function is partitioned into attractive domains for the corner points, which are convex polytopes.
cases of k = 2 and k = 3. It is also proven when monopoly is reached for a
particular feedback function and that the simplex for this function is partitioned
into attractive domains for the corner points, which are convex polytopes.