Any information on a toy economy with 3 types of agents in it I was thinking about a theoretical economy where there are 3 types of roles for the agents. They can be :

workers : produce good A
criminals : steal good A
cops : protects good A

without going into details, are they any theories around this type of economy and the different types of equilibrium that can be achieved, using different characteristics for agents, different rules etc...

This idea came from the fact that raising productivity could have perverse effects (raise criminality in this case) given certain conditions.

Also, do you have any tips on researching among existing economic theories for something that will describe an idea that you might have,
Becker has a very widely cited paper about crime that generally defines the literature, here.  

To examine your proposal, increases in productivity generally lead to higher wages in the legal sector, but could easily increase crime rates if they disproportionately increased the returns to crime. 

No agent modeling or network theory is needed for this to an accepted idea in the literature, but you're welcome to explore it if you think the consequences are somehow divergent from what I've outlined here! Furthermore, the actual task to -verify- his theory is very difficult. To search "the literature", I would search within the body of papers citing this particular Becker paper.