In this note we study a class of $2\times 2$ Polya-Eggenberger urn models, which serves as a stochastic model in biology describing cannibalistic behavior of populations. A special case was studied before by Pittel using asymptotic approximation techniques, and more recently by Hwang et al. using generating functions. We obtain limit laws for the stated class of so-called cannibal urns by using Pittel's method, and also different techniques.
"Analysis of a class of Cannibal urns." Electron. Commun. Probab. 16 583 - 599, 2011. https://doi.org/10.1214/ECP.v16-1669