5. Three players, P1, P2 and P3, are playing a game as described below. In a...

 

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5. Three players, P1, P2 and P3, are playing a game as described below. In a room, there are three doors, A, B and C. P1 hides behind a door. Then P1 and P2 enter the room not knowing Pl's choice. And P2 picks one door and opens it. If P1 is behind the door picked by P2, then the game is over and P2 wins. If P1 is not behind the door opened by P2, then P3 opens one of the two remaining doors. If P1 is behind the door picked by P3, then P3 wins. If P1 is not behind the doors opened by P2 and P3, then P1 wins. The winner receives 1 dollar and all others receive zero. (a) Represent the situation in a game tree. (3 points) (b) How many information sets P1, P2 and P3 have? Just write down the numbers. (1 point) 5. Three players, P1, P2 and P3, are playing a game as described below. In a room, there are three doors, A, B and C. P1 hides behind a door. Then P1 and P2 enter the room not knowing Pl's choice. And P2 picks one door and opens it. If P1 is behind the door picked by P2, then the game is over and P2 wins. If P1 is not behind the door opened by P2, then P3 opens one of the two remaining doors. If P1 is behind the door picked by P3, then P3 wins. If P1 is not behind the doors opened by P2 and P3, then P1 wins. The winner receives 1 dollar and all others receive zero. (a) Represent the situation in a game tree. (3 points) (b) How many information sets P1, P2 and P3 have? Just write down the numbers. (1 point)

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