Question

1. Consider the following game. Owen and Carter both write $1 or $3 on a piece of paper simultaneously. If both write the same amount, Owen wins and gets the amount written. If players write different amounts, Carter wins and gets $2. The loser gets nothing. Which of the following is true?

Group of answer choices

A- Owen has a dominant strategy.

B-There is no pure strategy Nash equilibrium.

C-In a Nash equilibrium, Owen writes $3.

D-Carter has a dominant strategy.

Consider the following scenario.

Suppose there are 2 seats on the bus, X and Y. Nathan and Benjamin each choose one seat. Both prefer seat X. Nathan chooses first. Benjamin chooses after observing Nathan’s choice. If both choose the same seat, Nathan cannot sit. Both prefer sitting to not sitting.

In the scenario above, which of the following is true?

Group of answer choices

A-There is no pure strategy Nash equilibrium.

B-Nathan chooses seat X in any Nash equilibrium.

C-Nathan chooses seat Y in any Nash equilibrium.

D-Nathan can choose seat X or Y depending on the Nash equilibrium.

Answer 1

Question 1

Payoff Matrix:

	1	3
1	(1,0)#	(0,2)*
3	(0,2)*	(3,0)#

Owen does not have any dominant strategy since 1 > 0 but 0 is not > 3. Option A is incorrect

- if Owen chooses to write $1, then the best response of Carter is to write $3

- if Owen chooses to write $3, then the best response of Carter is to write $1

Similarly,

- if Carter chooses to write $1, then the best response of Owen is to write $1

- if Carter chooses to write $3, then the best response of Owen is to write $3

Hence, there is no pure strategy nash equilibrium in this game

Option B is correct

Carter also does not have any dominant Strategy in this game. So, option D is also incorrect

Hence, Option B is the correct choice

Question 2

Option C is correct

Game Tree:

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