Section 1 Consider the following game between Liberty and McKenna. (Payoffs are

Question

Section 1 Consider the following game between Liberty and McKenna. (Payoffs are written with Liberty's first, then Mckenna's) 1. L5 points] McKenna Left Up 2, 3 3,4 Liberty Middle 5, 1 1,2 Down 4,3 2, 4 Consider the following statements about the game. i. Liberty has a dominant strategy ii. Liberty has no dominant strategies ii. McKenna has a dominant strategy iv. McKenna has no dominant strategies v. The game has a dominant strategy equilibrium vi. The game has a Nash equilibrium Now select the option which you think is correct, and explain why it is correct: a. Statements ii, iv and vi are true b. Statements ii, v and v are true c. Statements i, iii and v are true d. Statements i, iii and iv e. Statements ii, iii and vi

Explanation / Answer

When Liberty chooses UP , then Mckenna has more pay off in choosing RIGHT.

When Liberty chooses MIDDLE, then also Mckenna has more pay off in choosing RIGHT.

When Liberty chooses DOWN ,then also Mckenna has more pay off in choosing RIGHT.

So, this implies that Mckenna has a dominant strategy in choosing RIGHT.

When Mckenna chooses LEFT , then Liberty has more pay off in choosing MIDDLE .

When Mckenna chooses RIGHT, then Liberty has more pay off in choosing UP.

This implies that Liberty has no dominant strategy.

Nash Equilibrium is when both players best reponses intersect i.e (UP, RIGHT) .

Hence, option(e) i.e (ii), (iii) and (vi) are correct.

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