Question: This is the matching theory course Please help with the second and thirs tasks 2. In what follows, we will prove the following lemma in

This is the matching theory coursePlease help with the second and thirs tasks 2. In what follows, we will prove the following lemma in two steps: Lemma 1 A matching ,u. is group stable {fund

This is the matching theory course

Please help with the second and thirs tasks

$only {fit is (pairwise) stable. Proof of \"Only if" Direction. Suppose that$ a matching ,u. is pairwise stable, but also for contradiction that it

[u] is not group stable. Then it is blocked by a coalition

2. In what follows, we will prove the following lemma in two steps: Lemma 1 A matching ,u. is group stable {fund only {fit is (pairwise) stable. Proof of \"Only if" Direction. Suppose that a matching ,u. is pairwise stable, but also for contradiction that it [u] is not group stable. Then it is blocked by a coalition A and an outcome u'. a. [15 pts] Show that there exists at least one c E A. h. [15 pts] Show that there exists a students s E 01')_1{c) \\ (1401 (c) and a o E UJ}_1{S) \\{u'}_1[c) such that s >.; or.

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