What is the name of the game where in each round, another seat is eliminated?

Explanation

The game musical chairs starts with any number of players and one chair fewer. The chairs are arranged in a circle facing outward, and while music is playing, the players walkaround the chairs. When it stops, everyone must race to sit down in one of the chairs. The player who is left without a chair is eliminated from the game, and one chair is also removed to ensure that there will always be one fewer chair than there are players. The music resumes and the cycle repeats until there is only one player left in the game, who is the winner.