You'll find plenty of articles about the mechanics about free-to-play/freemium games there on games industry websites such as Gamasutra. Try the article below for a basic introduction to the mechanics behind the addictive properties:

http://www.gamasutra.com/blogs/JosephKim/20140323/213728/The...

As an aside, if you're investigating with the intent of building your own such games, be aware that A) the market is vastly oversaturated and B) people who make predatory freemium games are viewed with considerable contempt by the rest of the games industry.