  We start with the well-known game below: Two players hold a sheet of paper to
their forehead on which a positive integer is written. The numbers are
consecutive and each player can only see the number of the other one. In each
time step, they either say nothing or tell what number they have. Both of them
will eventually figure out their number after a certain amount of time. The
game is rather cooperative than competitive, and employs the notions of common
knowledge and mutual knowledge. We generalize this game to arbitrary (directed
and non-directed) simple graphs and try to establish for which graphs one or
both of them will figure out the solution, and how long they do need to find
it. We give a complete answer for the case of two players, even if they are
both allowed to discuss before the start of the game.
