The parameter b is privately known to player 2. player 1 knows only that b = 0 with probability 1/2 and b = 4 with probability 1/2. in other words, at the beginning of the game, nature chooses b = 0 with probability 1/2 and b = 4 with probability 1/2, and player 2 observes b. then the players simultaneously select x and y.