Feedback Interacting Urn Models

TL;DR

This paper introduces a novel class of feedback interacting urn models with deterministic and non-deterministic interactions, extending classical urn models to better understand complex interacting systems.

Contribution

It generalizes the classical urn model by incorporating feedback and interaction mechanisms, providing new frameworks for analyzing long-term behavior of interacting stochastic processes.

Findings

Introduced deterministic feedback interacting urn models.

Explored non-deterministic interaction behaviors.

Provided examples illustrating model consequences.

Abstract

We introduce and discuss a special type of feedback interacting urn model with deterministic interaction. This is a generalisation of the very well known Eggenberger and Polya (1923) urn model. In our model, balls are added to a particular urn depending on the replacement matrix of that urn and the color of ball chosen from some other urn. This urn model can help in studying how various interacting models might behave in real life in the long run. We have also introduced a special type of interacting urn model with non-deterministic interaction and studied its behaviour. Furthermore, we have provided some nice examples to illustrate the various consequences of these interacting urn models.