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# Game theory

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Ken and Gerard are roommates for a weekend and have succeeded in making their living quarters cluttered in very little time. Both would prefer to be in an uncluttered room, and if they both help to clean up each gets a utility of five. If one cleans and the other does not, the one who does not gets a utility of eight while the one who cleans gets a utility of zero because he had to do all the work. If both choose not to clean, they live in the mess and get one unit of utility.

Gerard

Clean Don't clean

Ken Clean
Don't clean

1.1. Gerard gets a payoff of either ______ from cleaning, depending on what Ken is doing.

A. 5 or 8

B. 5 or 0

C. 8 or 1

D. 0 or 1

1.2. Gerard gets a payoff of either ______ from not cleaning, depending on what Ken does.

A. 0 or 1

B. 8 or 1

C. 5 or 0

D. 5 or 8

1.3. Identify a dominant strategy for Ken (if he has one):

A. Ken does not have a dominant strategy

B. Clean

C. Don't clean

Mahala and Aruna are two teens who earn some money in their spare time babysitting toddlers in their neighborhood. Each girl can charge either \$15 or \$10 per hour for their services. If both charge \$15 an hour, each is hired for only three hours a week. If one charges \$10 while the other charges \$15, the less expensive babysitter is hired for eight hours a week, while the other is hired for only two hours a week. If both charge \$10 an hour, each is hired for five hours a week.

Provide values of the payoff matrix for this game between Mahala and Aruna, where the payoffs are expressed in terms of each individual's weekly earnings.

Aruna

\$15 \$10

Mahala \$15
\$10

2.1. Mahala gets a payoff of either ______ from charging \$15 an hour, depending on what Aruna charges.

A. \$45 or \$80

B. \$30 or \$50

C. \$80 or \$50

D. \$45 or \$30

2.2. Mahala gets a payoff of either ______ from charging \$10 an hour, depending on what Aruna charges.

A. \$45 or \$30

B. \$45 or \$80

C. \$80 or \$50

D. \$30 or \$50

3. The payoff matrix for the telephone game between Akbar and his mother is shown below:

Akbar's Mother

Call Wait

Akbar Call 0, 0 1, 2
Wait 2, 1 0, 0

Identify a dominant strategy for Akbar (if he has one):

A. There is no dominant strategy

B. Call

C. Wait