League of legends matching algorithm study

Hey, I’m an economics master student. We actually study fairness and efficiency aspects matching algorithms a lot. But those studies are generally applied to school/hospitable/labor settings. I need a term paper and am really interested in the study of gaming matching algorithms. Aspects of the matching could be users experience,strategic manipulation, fairness and efficiency etc. It’s a bit theoretical to come up with proper definitions and theorems for characterize a matching algorithm.

In order to proceed, I need a very general description of how exactly it works, like what it does behind the curtain. Can anyone share any resources for me to look into this? Thank you very much.