Question about a game procedure

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Hi there :)
I'm making a session based multiplayer (like brawl-stars / clash royal) where a game has a very specific procedure:
1. declaring players.
2. starting game.
3. game ends.
4. declaring winners.
5. receiving rewards.

My question is who manages the game procedure..
Is the admin of the room managing the procedure and everyone is saving the state in case the admin quits and they'll be picked as an admin? or how do most developers implements this stuff?

Thanks in advance :smile: