Consider a marriage problem with three men m1,m2,m3 and three women w1,w2,w3

Consider a marriage problem with three men m1,m2,m3 and three women w1,w2,w3. Suppose all men see all women as acceptable, and all women see all men as acceptable. Moreover, suppose that all men’s top choice is the same. If this is the case, at most how many stable matchings could there be?

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Expert Solution

Conditions given are -

Number of women = 3 (W1, W2 & W3)
Number of men = 3 (M1, M2 & M3)
All Men as well as all Women are acceptable to each other.
all men's top choice is the same.

According to last condition, all 3 men would choose one particular women who will become the top choice of all men. However, that one women will only choose one out of three men to marry. Suppose that the woman who is choosen by all men as their top choice is W1. Thus there are following stable matchings could possible -

M1 – W1
M2 – W1
M3 – W1

Hence, 3 stable matchings could be possible.

Rahul Sunny answered 1 year ago

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