While at the$$ airport, you hear over the loudspeaker an offer to be bumped off your current flight in exchange for a$$ $$100$ travel credit. After it becomes clear that nobody will take this$$ offer, the offer is increased to$$ $$200.$ A few minutes$$ later, the airline offers$$ $$300$; then$$ $$400$; and so on$.$ Individually, each passenger wants to take the$$ offer, but$$ collectively, it is best for people to hold out. The strategic dynamic can be modeled with a$$ two$-$player "centipede$$ game."