Question: 3 . 2 . 1 1 . ( * ! ) Prove that if manx is paired with woman a in some stable matching, then

3.2.11 . (*!)

Prove that if manx is paired with woman

a

in some stable matching, then a does not reject

x

in the Gale

-

Shapley Proposal Algorithm with men proposing. Conclude that among all stable matchings, every man is happiest in the matching produced by this algorithm.

(

Hint: Consider the first occurrence of such a rejection.

)

3.2.11.(*!) Prove that if manx is paired with woman a in

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