Elizabeth and Johnny are playingHide and Seek. Elizabeth is hiding, and Johnny is searching for her. The payoff to Elizabeth from successfully hiding is 5 and from being caught is 2. For Johnny, the payoff from finding Elizabeth is 9, and from not finding her is 4. Elizabeth can hide inLibrary,Karl Popper,orMeremere.Because Johnny has a leg injury from his recent weekend party, he cannot search for her at all places. Suppose Johnny can search any two places so that he has three pure strategies:Library and Karl Popper,Library and Meremere, orKarl Popper and Meremere. Use the concept of Mixed Strategy Nash Equilibrium and answer the questions.

Probability of Elizabeth choosing her pure strategyLibrary:

a.

1/3

b.

2/3

c.

3/4

d.

3/5

e.

4/5

Probability of Elizabeth choosing her pure strategyKarl Popper:

a.

1/3

b.

2/3

c.

3/4

d.

3/5

e.

4/5

Probability of Johnny choosing his pure strategyLibrary and Meremere:

a.

1/3

b.

2/3

c.

3/4

d.

3/5

e.

4/5

Expected payoff of Elizabeth from choosing her pure strategyLibrary:

a.

3

b.

5

c.

7

d.

9

e.

11