In the following three-player game, Player 1 chooses a row (U or D), Player 2 chooses...

 

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In the following three-player game, Player 1 chooses a row (U or D), Player 2 chooses a column (L or R), and Player 3 chooses a matrix (a, B). Find all pure and mixed strategy Nash equilibria of this game. { Hint: The logic is extended from the two player games. Write down the expected utilities of players when they use a pure strategy to face their opponents who are miring between their actions. } PI 2 PI 2 L R L R U (1,1,1) (0,0,0) (0,0,0) D (0,0,0) (0,0,0) U PI 1 PI 1 D (0,0,0) (0,0,0) (2,2, 2) In the following three-player game, Player 1 chooses a row (U or D), Player 2 chooses a column (L or R), and Player 3 chooses a matrix (a, B). Find all pure and mixed strategy Nash equilibria of this game. { Hint: The logic is extended from the two player games. Write down the expected utilities of players when they use a pure strategy to face their opponents who are miring between their actions. } PI 2 PI 2 L R L R U (1,1,1) (0,0,0) (0,0,0) D (0,0,0) (0,0,0) U PI 1 PI 1 D (0,0,0) (0,0,0) (2,2, 2)