In a recent post I described stopping games in continuous time; I mentioned that in this class of games, an equilibrium exists if there are at most two players, and it does not necessarily exist if there are at least three players. David Rahman, who visited Tel Aviv, asked me about the existence of correlated equilibrium in stopping games in continuous time. My first guess was that the three-player game that I described in that post had no correlated equilibrium. Last night I did the necessary calculations, and I was surprised to learn that this game possesses a correlated equilibrium: a mediator chooses a pair of players, each pair is chosen with probability 1/3, and that pair should stop at time 0, while the third player continues. There are additional correlated equilibria, but this is the simplest one. Does there always exist a correlated equilibrium in stopping games in continuous time? I bet that the answer is negative, but I am ready to be surprised again. Can anyone come up with a proof that a correlated equilibrium always exists, or with an example of a game without a correlated equilibrium?