The Free Rider

My son was going to his first chess tournament yesterday. The flier said that he needed to have a chess clock. I forgot about that.
My wife reminded me on the morning of the tournament that he needed a clock.
“Would any clock do?”
“No, it is a special clock. I will find a store and bring it to you at the tournament.”
My wife and I went on-line to see what stores might have chess clocks.
“Why wouldn’t a regular clock work?”
“It is a special clock that has two buttons. When one player makes a move, he pushes the button and his opponent’s clock starts.”
“Do both players need a clock?”
“No, they just use one clock.”
“Then free ride. Pah, why didn’t you tell me that before? I could have eaten breakfast.”
So what is the equilibrium of the who-brings-a-clock-to-the-tournament game?