There is a network of ~61k full nodes (computers) that enforce the consensus rules of Bitcoin. Most of these nodes are not controlled by miners.
When a miner solves a special puzzle that all the full nodes enforce, they get rewarded in (inflation + transaction fees) for their efforts.
The Bitcoin code that enforces the rules insures that these miners cannot produce much more bitcoin ahead of schedule because of the "difficulty algorithm" which dynamically adjusts both ways making it harder to solve the right puzzle or easier to solve it depending upon how much mining was done during the previous 2016 blocks (~2 weeks) to ensure that a predictable and controlled amount of bitcoin are created
https://en.bitcoin.it/wiki/Controlled_supply
Another analogy is this - The judges that control the rules of the game are the full nodes, there is a single trophy (block reward) for those who win every ~10 minutes of the game, and anyone can compete in the game but the more players that decide to join doesn't create more trophies to win but simply makes it harder automatically due to more competition for that trophy.