Represent the following game in the extensive form. there are three players, numbered 1, 2, and 3. at the beginning of the game, players 1 and 2 simultaneously make decisions, each choosing between x and y.
if they both choose x, then the game ends and the payoff vector is (1, 0, 0); that is, player 1 gets 1, player 2 gets 0, and player 3 gets 0. if they both choose y, then the game ends and the payoff vector is (0, 1, 0); that is, player 2 gets 1 and the other players get 0. if one player chooses x while the other chooses y, then player 3 must guess which of the players selected x; that is, player 3 must choose between 1 and 2.
player 3 makes his selection knowing only that the game did not end after the choices of players 1 and 2. if player 3 guesses correctly, then he and the player who selected x each obtain a payoff of 2, and the player who selected y gets 0. if player 3 guesses incorrectly, then everyone gets a payoff of 0.