<p>Can you help with this statement?</p>
<p>Let N be a set of agents in a two-sided matching market. Apply a
version of the deferred acceptance alghoritm and suppose it
produces the allocation µ in which agent i is matched with itself.
Suppose now that we delete agent i from the set of agents and
from the preferences of each of the other agents.
(a) is µ stable also in the new model?
(b) If we apply the same version of deferred acceptance in the new
model, will the outcome will be necessarily the same as before (that
is the allocation µ)?</p>
<p>I think that answer (a) is because if i is matched with itself is impossible to find a blocking coalition.
I think also that the answer (b) is yes. Because if it is unmatched it means that either she prefers to remain alone or no one wants her. Any suggestions?</p>

CC BY-SA 4.0
2023-05-25T16:41:23.840Z
Are you talking about 1-1 matchings?
Michael Greinecker
CC BY-SA 4.0
2023-05-25T16:42:59.737Z
Yes, 1:1 matching
userF
CC BY-SA 4.0
2023-05-25T16:46:18.453Z
If you have learned that already, this follows from side optimality and the lone wolf/rural hospital theorem.
Michael Greinecker
CC BY-SA 4.0
2023-05-25T17:08:24.850Z
Can you give me some references on this? I am not aware of it
userF
CC BY-SA 4.0
2023-05-25T17:10:12.213Z
I learned this thigs first from the game theory book by Maschler, Solan, and Zamir
Michael Greinecker
<microeconomics><mechanism-design>
Deferred Acceptance Algorithm
userF
# Deferred Acceptance Algorithm

(Asked by: username_0 on 2023-05-25)

Can you help with this statement?

Let N be a set of agents in a two-sided matching market. Apply a
version of the deferred acceptance alghoritm and suppose it
produces the allocation µ in which agent i is matched with itself.
Suppose now that we delete agent i from the set of agents and
from the preferences of each of the other agents.
(a) is µ stable also in the new model?
(b) If we apply the same version of deferred acceptance in the new
model, will the outcome will be necessarily the same as before (that
is the allocation µ)?

I think that answer (a) is because if i is matched with itself is impossible to find a blocking coalition.
I think also that the answer (b) is yes. Because if it is unmatched it means that either she prefers to remain alone or no one wants her. Any suggestions?

**Tags:** microeconomics, mechanism-design

> **Comments:**
> **username_1**: Are you talking about 1-1 matchings?  
> **username_0**: Yes, 1:1 matching  
> **username_1**: If you have learned that already, this follows from side optimality and the lone wolf/rural hospital theorem.  
> **username_0**: Can you give me some references on this? I am not aware of it  
> **username_1**: I learned this thigs first from the game theory book by Maschler, Solan, and Zamir  

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## 0 answers

