The first step of any data modeling exercise is to build a diagram to show the entities in your application and how they relate to each other.
In the application, you have the following entities:
User
Game
UserGameMapping
A User entity represents a user in the application. A user can create multiple Game entities, and the creator of a game will determine which map is played and when the game starts. A User can create multiple Game entities, so there is a one-to-many relationship between Users and Games.
Finally, a Game contains multiple Users and a User can play in multiple different Games over time.
Thus, there is a many-to-many relationship between Users and Games. You can represent this relationship with the UserGameMapping entity.
With these entities and relationships in mind, the entity-relationship diagram is shown below.

Next, we will take a look at the access patterns the data model needs to support.