Consider the following two player game. Player 1 moves first and chooses TOP or BOTTOM. If player 1 chooses TOP then the game ends and both Player 1 and Player 2 get $2 each. But if Player 1 chooses BOTTOM, then Player 2 gets the move and Player 2 can respond with LEFT or RIGHT. If Player 2 chooses LEFT then Player 1 gets $1 while Player 2 gets $4. But if Player 2 chooses RIGHT, then Player 1 gets $3 and Player 2 gets $1.
(a) Draw the game tree for this game. Clearly label your tree with the moves and the payoffs to each player. (b) If you solve this game using backward induction, then what would be the outcome of this game? That is, what is the subgame perfect equilibrium? Explain briefly how you arrive at your answer.

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The Answer of Consider the following two player game. Player 1 moves first and chooses TOP or BOTTOM. If player 1 chooses TOP then the game ends and both Player 1 and Player 2 get $2 each. But if Player 1 chooses BOTTOM, then Player 2 gets the move and Player 2 can respond with LEFT or RIGHT. If Player 2 chooses LEFT then Player 1 gets $1 while Player 2 gets $4. But if Player 2 chooses RIGHT, then Player 1 gets $3 and Player 2 gets $1.
(a) Draw the game tree for this game. Clearly label your tree with the moves and the payoffs to each player. (b) If you solve this game using backward induction, then what would be the outcome of this game? That is, what is the subgame perfect equilibrium? Explain briefly how you arrive at your answer.

Consider the Following Two Player Game