# (Solved Homework): Game Threory 1) In a 2 x 2 game, show an example of a strategy profile where both players…

1) In a 2 x 2 game, show an example of a strategy profile where both players are choosing a Weakly Dominant Strategy, but neither player is playing a strict best response to the other’s strategy.

2) Consider the game below.

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Player 1(left) Player 2(top)

 C D E F A 1,2 3,1 0,0 5,3 B 1,1 1,3 0,2 4,2

(a) Which outcome(s) would you predict in this game assuming only that both players are rational and that Player 2 knows that Player 1 is rational?

(b) Which outcome(s) would you predict in this game assuming that the rationality of both players is common knowledge?

A>

 C D E F Step 1 Step 2 A 1,2 3,1 0,0 5,3 Player 1 A Player 2 F B 1,1 1,3 0,2 4,2 Player 1 B Player 2 D C D E F A 1,2 3,1 0,0 5,3 Player 2 C Player 1 A or B B 1,1 1,3 0,2 4,2 Player 2 D Player 1 A Player 2 E Player 1 A or B Equilibrium Player 2 F Player 1 A C D E F A 1,2 3,1 0,0 5,3 A,F B 1,1 1,3 0,2 4,2 B,D

If Player 1 is rational he will always go for A.

So A,F

So player 2 will go for F no matter what Player 1 selects.

B.

Using the above, the rational strategy is A,F

Player 1 has A as the best option.

Player 2 can go for F or D, But as he is aware of Player 1 rationality, he will always go for F

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