Represent the game in the extensive form

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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 obtains a payoff of 2, and the player who selected “Y” gets 0. If player 3 guesses incorrectly, then everyone gets a payoff of 0.

Reference no: EM13997369

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