Fair Division Fair Division What is a fair way for 2 people to - - PowerPoint PPT Presentation

SLIDE 1

Fair Division

SLIDE 2

Fair Division

• What is a fair way for 2 people to split a heterogenous, divisible

good?

• Why not 50/50?
• I Cut, You Choose Protocol
• Player I told to split the good into two pieces A and B such that v(A) = v(B) =

½ v(A U B).

• Player II picks his favorite of A and B.
• Player I takes the other piece.

SLIDE 3

Formal Model

it

SLIDE 4

Allocation

Ai Aa

An

is

proportional

Ai pieceplayeri

f

ti

v

Ai

th

gets

envy free y

ti j

v

Ai

4 Aj

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access to

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is thru 2 typesof

queries

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042

cut

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queries

SLIDE 5

How to

measure

complexity

• f

a

division protocol

wanti

running fine

as fn of

n

Standard model e

i's

is

thru

2 types ofqueries

Eval

x y

playeri returns Vicky

cut

his

I't's

How many queries

does

a

protocol take I

Cut

Yon Choose

2gueries

With

ducde

conquer

can get

proportional

woc.us

n

queries

SLIDE 6

SLIDE 7

Is

3

SLIDE 8

4

al

as

I 04

i

s

s

SLIDE 9

O

O

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SLIDE 10

5 queries

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Taylor

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ab

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Aziz

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cuts

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SLIDE 11

C

Truthfulness

Fis

truthful y

no

player can T

their

utility for outcome

by misrespondig to

any query

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their

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deterministic mech for awaiting

is

truthful

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approx

proportional

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B

Bn

nonconstructive

SLIDE 12

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G CD

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• f bundles

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SLIDE 13

Fair

division with

indivisible

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for item j

j

m

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why

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SLIDE 14

Album

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Au is

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up

to

• ne good

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SLIDE 15

A

SLIDE 16

Auctions

• Ancient mechanism for buying and selling goods.
• In modern times, used for many economics transactions.
• In the age of the Internet, we can buy and sell goods and services via

auctions online, e.g. using eBay

• Companies. like Google and Microsoft use ad auctions to sell

advertisement slots that will appear alongside your search results.

• All major search engines and social networking sites (e.g. Facebook)

make most of their money from running real-time auctions used to sell online advertisements.

• Consequence: auctions are a major driver of modern Internet

economy.

• Why use an auction as opposed to simply fixing prices?

SLIDE 17

Why might a sell user an auction as opposed to fixing a price?

• Because sellers don’t know how much buyers value their goods and

don’t want to risk setting prices that are too low (leaving money on the table) or too high (nobody buys).

• Auction is technique for dynamically setting prices.
• In Internet settings, where the participants in the auction are

computer programs or individuals who don’t know each other, price- setting is particularly difficult and this is what motivates auctions.

SLIDE 18

Single

item

auctions

Seller

w

single good

h

strategic

bidders

b

rulesspecify

who

wins

Rhofumbuffderpass

each bidder has

a private

value

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everyone pays

what they

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anchor

y

Vickrey anchen

submit

sealed bids

Lemma Ina

s

d is

a dominant

gy

to bid

truthfully

ie

set bi

vi

dominant strategy incentive

compatible

Dsl C

Proof

Fix

bids

b i

let

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IIB

SLIDE 19

Y tmhfully

chievesths

Truthful

cod

agents

don't

need

to

strategize 2ndprice anchor

guarantees

that

Hen ends

up in

the hands

• f

the player

who

Valves

it the most

social

welfare surplus efficiency

sum

• f

utilities

• f all

participants

including

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