A fun discussion on characterizing the motivations of gamers is "Engines of Play: How Player Motivation Changes over Time" [1]. I'm not hugely in love with the sorts of models, he builds, but any sort of structure is useful for kickstarting your thought.

The big win in that talk, though, was that he introduced me to Self-Determination Theory[2]. A very convincing theory on motivation. It's introduced in the talk at 38:05.

[1]: https://www.gdcvault.com/play/1023329/Engines-of-Play-How-Pl... [2]: https://en.wikipedia.org/wiki/Self-determination_theory