(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?

Expert Answer

Answer

	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.

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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