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. In pursuing his own self-interest, Hector will

	a.	clean whether or not Bart cleans.
	b.	refrain from cleaning whether or not Bart cleans.
	c.	clean only if Bart refrains from cleaning.
	d.	clean only if Bart cleans.

Answer 1

Answer to the question is option d) neither Hector nor Bart cleans.
Reason is :-
Given the payoff matrix , the nash equilibrium to this game is that both Hector and Bart don't clean their apartment. This is because ;
The equilibrium can be explained as :-
If Hector considers to clean , the best decision for Bart , given Hector decides to go for cleaning , is to go for Don't clean. This is because for Bart 10 is greater than 7 , so he goes fo not cleaning. Now if Bart dont clean , the best strategy for Hector is not to clean as 5 is greater than 2. So it is not a nash equilibrium.
If Hector considers to dont clean , the best decision for Bart , given Hector decides to dont clean , is to go for dont clean as for Bart 4 is greater than 2. Now if Bart dont clean , the best strategy for Hector is to dont clean as 10 is greater than 5 for Hector. So it is the best strategy for both Hector and Bart to dont dont .
So dont clean is the best strategy for both Hector and Bart and they it gives the maximum payoff to both given the strategy of other. So this is the Nash Equilibrium of the game.

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