Consider the following game, where the rows represent the actions available to p

Question

Consider the following game, where the rows represent the actions available to player 1 and the columns represent the actions available to player 2: (a) Prove that there is no mixed strategy of player 2 of the form (p, 1 - p, 0) which strictly dominates the pure strategy R. (b) Prove that there is no mixed strategy of player 2 of the form (0, p, 1 - p) which strictly dominates the pure strategy L. (c) Find the range of values of p for which the mixed strategy (p, 0, 1 - p) strictly dominates the pure strategy C. (d) Based on your answers to parts (a) -(c), write down the set of rationalizable strategies each player. Two players play the BoS game with payoffs measured in dollars and given by the following matrix.

Explanation / Answer

1.

a) When player 1 choose the strategy U and player 2 chooses the strategy R, Player 1 get the pay off 6.

Tha maximum pay off for player 1 from strategy D is 4 , against strategy L of player 2.

Since the hoghest pay off is 6 under strategy R of player 2, The pure strategy for Player 1 is U against the strategy R of player 2. Hence there is no mixed strategy for player 1.

b) When player 2 choose the strategy L and player 1 chooses the strategy U or D ,best pay off of Player 2 is 5.

When player 2 choose the strategy C and player 1 chooses the strategy U or D, Player 2 get the pay off 3 against U.

When player 2 choose the strategy R and player 1 chooses the strategy U or D, Player 2 get the pay off 4 against D.

Tha maximum pay off for player 2 is from strategy L which is 5, against strategy U of player 1.

Hence The pure strategy for Player 2 is L , against the strategy U of player 1.

Hence there is no mixed strategy for player 2.

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