There are n≥2 players P1,P2,...,Pn, each of them having a finite alphabet A1,...,An, and there is a probability distribution p on A=A1×ëëë×An. The players want to choose a∈A according to p in such a way that Pk knows only the kth component, ak, of a. This can be done with the help of an impartial person or ‘fortune’ who chooses a∈A according to p and informs Pk on ak only. But what happens if no such person is available? Can the players find a procedure that replaces fortune? It is proved here that the answer is yes when n≥4. As an application it is shown that a correlated equilibrium of a noncooperative n-person game (n≥4) coincides with a Nash equilibrium of an extended game involving, in addition, plain conversations only.
