100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
ECON0027 Week 10 $9.29   Add to cart

Class notes

ECON0027 Week 10

 15 views  0 purchase
  • Course
  • Institution

In depth notes on ECON0027 Week 10

Preview 2 out of 5  pages

  • May 21, 2024
  • 5
  • 2022/2023
  • Class notes
  • Nikita roketskiy
  • All classes
  • Unknown
avatar-seller
Cooperative games
Week 10
Ch 8

De nitions
Although agents can coordinate, they are still rational so maximise their own payo
Players N t nl


Core
an 75astiesasian
Or, an action of a grand coalition y is in the core if there exists no coalition S and action x that this
coalition can take such that
ie. it is Pareto e cient



Games in characteristic form
HSEN Us isthevalueofgroups
t aken
Action
bysix I pearls soti
I
ieanaction
coalition
cantareisadivision

ofthevalue
Core HEIR neVIN
ASEN v15
so
Two players
N1,2 v110.5 v120.6 v41.23 1
V11Ov120,411,2311
Core x Y sax1
x villa's
serial0.6
core
Mt x vill0
L exist
doesn't



Three players
11 12,3 vlil1tieN.ir13 4 v12 5 v1233 VIN110
t one sansa
I a sexy
amino axes t
x xe5
x x 4

ng a É
Three player with symmetric payo s
lilb vlijka.IN10


I
the'iastelementifenecoretobe canbeusedtotes ifcoreisempty
invalidated.seyfgYYy

, Allocation of objects
1141 n M1 m e strictpreferencesof ioverM
trade
coalition whenasubset players o bjects
is of
amatching MN Moo ieagent givena
either orn ot
house


tinsuchthat MilMl

Serial dictatorship algorithm
• Rank the agents
• The rst agent picks their preferred object,
• Remove their choice and the next agent chooses

Proof by contradiction that this is a core:
• Suppose agent 1 prefers object 1, which was unavailable to them, to the object 2 matched to
them
• The person who chose object 1
◦ Object 1 was the best object in their view, so giving them object 2 would decrease their
welfare
◦ Preferred another object that was unavailable to them
‣ This would require giving them the object unavailable to them
‣ The chain of improvements would continue until at least one person, the person ranked
rst, received their best choice

For any core allocation there is at least one person who is allocated their rst best choice, proof by
contradiction:
• Imagine a core allocation in which no agents have their favourite object, and they all indicate
whose object they’d prefer
• There is a trading cycle which would be a Pareto improvement
• This is a contradiction, as the initial allocation cannot be in the core if there can be a Pareto
improvement

Any Pareto e cient outcome can be generated by a serial dictatorship mechanism, proof:
• From a Pareto e cient allocation, select all agents whose receive their rst best choice (these
exist due to proof above) and assign them top rank
• Remove them and their objects, and the allocation is also Pareto e cient
• Repeat this with the remaining agents having their best of the objects remaining, until there are no
agents left
• Applying serial dictatorship allocation with the resulting ranking will obtain the allocation in
question


Allocation of objects with endowments- top trading cycles
N t n M 1 n InitialmatchingMo
Core
Misinthecoreif ISenFmforSMos tiesMitMit e.g

I
i
Top trading cycles: 4 5
s 7 Rounds
• Agents indicate their favourite objects
• Find all cycles and trade (cycles always exist due to graph theory)
3 6 rounds
• Remove everyone who traded 6 1

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller zctpfru. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $9.29. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

66579 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$9.29
  • (0)
  Add to cart