Wiktionary
n. (context idiomatic English) A situation in which two individuals attempting to contact each other by telephone repeatedly do not get a live person and instead trade messages, such as by voice mail.
Wikipedia
Phone tag is a phenomenon in which two parties attempt to contact each other by telephone, but neither is able to get a hold of the other for a conversation. Both parties may leave a message on the answering machine or voicemail of the other, and request a call back. This continues for a period of time, often with the two parties exchanging attempts to have a real-time conversation. The name derives from the playground game tag, where players chase one another in turn.
Phone tag became common in the 1980s with the advent of messaging technologies and caller ID. It was seen as having advantages in that people can leave and receive messages at their convenience rather than having to find a common time with the other party to have a conversation.
Phone tag is the art of calling a person only to receive said persons' answering machine. They then call you back only to now receive your answer machine. This process is repeated until one person reaches the other, or both parties give up. It's just like playing a game of tag from when you were young.
With phone tag being possible, people have a choice of when they want to return calls they have received. They may also decide which calls they wish to return and which to not (similar to call screening). Many recipients of messages simply choose to not return certain calls.
Usage examples of "phone tag".
Her right ear was sore from being pressed so long against the receiver, and she had the beginnings of a headache that strenuous games of phone tag always engendered.
It was a good day to make phone calls, and I started a nice game of phone tag as I was forced to leave messages on everyone’.
We'd been playing phone tag the past two days, Laxton being inexplicably absent from his office.
They'd met last Saturday, but talked on the phone Monday, Tuesday and Wednesday, then played phone tag.
Play more phone tag with other divisions, neighboring cities, in case Pelley and/or Nut Buddy has been a bad boy somewhere else.