Question

Monica and Isabel are roommates who, on this particular Saturday morning, are trying to decide what scarf to wear. Each has a Burberry scarf (which we’ll denote B), a tan scarf (denoted T), and a mauve scarf (denoted M). They care about the scarf but also about whether they end up wearing the same or different scarves. The preference ordering (from best to least preferred outcome) for Monica is: (1) she wears B and Isabel wears T or M; (2) she wears T and Isabel wears B or M; (3) she wears B and Isabel wears B; (4) she wears T and Isabel wears T: (5) she wears M and Isabel wears M; and (6) she wears M and Isabel wears B or T. Isabel’s preference ordering is: (1) she wears T and Monica wears B or M; (2) she wears M and Monica wears B or T; (3) she wears T and Monica wears T; (4) she wears M and Monica wears M; (5) she wears B and Monica wears B; and (6) she wears B and Monica wears T or M. Applying the IDSDS, which scarves will be worn?

Answer 1

Monica wears B and Isabel wears T.

Explanation:

Let each scarf combination give a certain payoff depending on the rank assigned to them. The higher the rank to the combination, the higher the assigned payoff and the higher the satisfaction recieved from it.

The ranks and payoffs are as follows-

Rank 1= Payoff 6

Rank 2= Payoff 5

Rank 3= Payoff 4

Rank 4= Payoff 3

Rank 5= Payoff 2

Rank 6= Payoff 1

For example, if Monica wears T and Isabel wears M, the combination is ranked 2nd for Monica and 2nd for Isabel. As such they will recieve the same payoff 5 from it.

The different combinations will give the following payoffs to them -

		Isabel
	Scarf	B	T	M
Monica	B	4,2	6,6	6,5
T	5,1	3,4	5,5
M	1,1	2,6	1,3

Lets examine the choices for Monica holding Isabel's choices constant-

If Isabel choses B, Monica should chose T as it maximizes her payoff

If Isabel choses T, Monica should chose B as it maximizes her payoff

If Isabel choses M, Monica should chose B as it maximizes her payoff

As we can see, Monica should not chose M regardless of the choice made by Isabel. Therefore, M is strictly dominated and can be eliminated.

The remaining choices and their payoffs are-

		Isabel
	Scarf	B	T	M
Monica	B	4,2	6,6	6,5
T	5,1	3,4	5,5

Examining Isabel's choices holding Monica's choices constant-

If Monica choses B, Isabel should chose T as it maximizes her payoff

If Monica choses T, Isabel should chose M as it maximizes her payoff

Isabel never choses B regardless of choices made by Monica. Therefore, B is strictly dominated and can be eliminated.

The remaining choices are-

		Isabel
	Scarf	T	M
Monica	B	6,6	6,5
T	3,4	5,5

Examining Monica's choices-

If Isabel choses T, Monica should chose B

If Isabel choses M, Monica should chose B

Monica never choses T and it can be eliminated.

		Isabel
	Scarf	T	M
Monica	B	6,6	6,5

Examining Isabel's choices-

If Monica choses B, Isabel should chose T.

As M is not chosen by Isabel, it can be eliminated.

		Isabel
	Scarf	T
Monica	B	6,6

The only remaining choices are Monica wears B and Isabel wears T. This combination is ranked 1 for both and gives a payoff of 6 to both.

Therefore, Monica will wear scarf B and Isabel will wear scarf T.