3NF and many to many table mysql

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As part of an assessment I need to build a site in PHP that relies on a database, the site can be on anything we want. The only restrictions on the site is the database must have a minumum of seven tables, must be in third normal form and have at minimum one many to many table.

Below is the Schema I have sofar, I am hoping people would be willing to tell me where it is not in third normal form, or if my many to many table (games) will not work.

I have an understanding of third normal form in that each item must be reliant on the primary key there to be no candidate key.

database schema

Thoughts?

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