Matching

Question 1

What is a matching market

Answer 1

market where there is no monetary transactions (and thus no price)

example:
- School assignment
- Medical match
- Allocation of dorms

Question 2

What is the stability in a matching problem

Answer 2

absence of blocking pairs

Question 3

What are the steps of Deferred Acceptance

Answer 3

Step 1: Each man proposes to his most preferred, acceptable woman (if a man finds them all unacceptable he remains single)

women either holds the offer or rejects it

Step 2: Each men whose offer was rejected in the last round proposes a new offer to the women he deems acceptable.

the women still has the same choice as earlier

Finally: Each woman is matched to the man whose offer she was holding

Question 4

Is the outcome of the deferred acceptance necessarily rational?

Answer 4

Yes, if it is not stable then there is a blocking pair

Question 5

Is Deferred Acceptance strategy proof for both sides?

Answer 5

No,

sometimes it is better to lie in order to be with your true first choice and sometime it is better to be truthful.

In general, when submitting your preference first, it is better to be truthful. Therefore, there is an advantage to pick 1st.

Question 6

How is a matching stable

Answer 6

If it is individually rational, via deferred acceptance, and if it isn’t blocked

Question 7

Why does stability matters

Answer 7

Because it’s fair and it makes it so that there’s no malicious plans from either the hospitals or the doctors

it also makes it so that it is safe for participants: No risk to delay matching decisions

Without the centrelized market in the deferred acceptance competitions with hospitals led to unravelling