I do not have an example of a religious story but a couple of references that support the theme you refer to.
The Evolution of Cooperation by Robert Axelrod discusses a simulation he performed with different strategies with different levels of cooperation and defection. This would provide a technical template for "violence begets violence", constant defection by bullies.
Another document that might add context is by Professor Terry Williams of Strathclyde University, "Viscious Circles of Parallelism", although this is SD applied to delay and disruption in large turnkey proejcts, one could apply the framework to social interaction with the resource shortfall being respect and consideration.
They are not exactly what you are looking for but might help.