musical chairs, play

¹

play musical chairs

²

Idioms and Phrases

Move around from position to position, such as the jobs in an organization. For example, Bob took over for Tom, who took over for Mary, who got Bob's title—the boss loves to play musical chairs with the staff . This expression alludes to the children's game in which children walk around a number of seats while music plays, and there is one less chair than players. When the music stops the players must sit down, and the player who is left standing is eliminated. Then another chair is removed, and the game goes on until only one player is left sitting. [c. 1900]

Example Sentences

Some have suggested Hillary play musical chairs with Joe Biden in a second term.

From The Daily Beast