Question: Consider a 3-player game. The first player P1 moves first and chooses a number x ? 0. Then, the second player P2 and third player

Consider a 3-player game. The first player P1 moves first and chooses a number x ? 0. Then, the second player P2 and third player P3 play a simultaneous move game where P2 chooses y ? 0 and P3 chooses z ? 0. Their payoffs are as follows:

ui(x, y, z) = 4xz - 4x - 2-2 u2(x, y, z) = x y + 2y - 5yz us(x, y, z) = 2yz - 2x22 - 22 1. Represent the extensive form of this game. 2. Find the subgame perfect Nash equilibrium of this game

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