Figure 17-3. Hector and Bart are roommates. On a particular day, their apartment needs to be cleaned. Each person has to decide whether to take part in cleaning. At the end of the day, either the apartment will be completely clean (if one or both roommates take part in cleaning), or it will remain dirty (if neither roommate cleans). With happiness measured on a scale of 1 (very unhappy) to 10 (very happy), the possible outcomes are as follows:
-Refer to Figure 17-3. The dominant strategy for Hector is to
A)clean, and the dominant strategy for Bart is to clean.
B)clean, and the dominant strategy for Bart is to refrain from cleaning.
C)refrain from cleaning, and the dominant strategy for Bart is to clean.
D)refrain from cleaning, and the dominant strategy for Bart is to refrain from cleaning.

Question

Figure 17-3. Hector and Bart are roommates. On a particular day, their apartment needs to be cleaned. Each person has to decide whether to take part in cleaning. At the end of the day, either the apartment will be completely clean (if one or both roommates take part in cleaning), or it will remain dirty (if neither roommate cleans). With happiness measured on a scale of 1 (very unhappy) to 10 (very happy), the possible outcomes are as follows: 
-Refer to Figure 17-3. The dominant strategy for Hector is to
A)clean, and the dominant strategy for Bart is to clean. 
B)clean, and the dominant strategy for Bart is to refrain from cleaning. 
C)refrain from cleaning, and the dominant strategy for Bart is to clean. 
D)refrain from cleaning, and the dominant strategy for Bart is to refrain from cleaning.

Quizplus · Accepted Answer

If Hector chooses to clean, he will be happier if Bart also cleans, resulting in a payoff of 8. However, if Bart refrains from cleaning, Hector will be unhappy with a payoff of 1. Thus, cleaning is not a dominant strategy for Hector.
Similarly, if Bart chooses to clean, he will be happier if Hector also cleans, resulting in a payoff of 8. However, if Hector refrains from cleaning, Bart will be unhappy with a payoff of 1. Thus, cleaning is not a dominant strategy for Bart either.
If both Hector and Bart refrain from cleaning, they both receive a payoff of 6, which is better than receiving a payoff of 1 if they choose to clean alone.
Therefore, the dominant strategy for both Hector and Bart is to refrain from cleaning, leading to a joint payoff of 6. Thus, the best choice is to not clean.