Reference no: EM131814916

Represent the following game in the extensive form. There are three players, numbered 1,2,3. 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 gets 0. If one player chooses "X" while the 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 obtains a payoff of 2, and the player who selected "Y" gets 0. If the player 3 guesses incorrectly, then everyone gets a payoff of 0.