Incentives in Computer Science One sided matching TTCA Kidney - - PowerPoint PPT Presentation

SLIDE 1

Incentives in Computer Science

One sided matching

TTCA

Kidney exchange

SLIDE 2

PARTICIPATION

• Please do it!!!!!!!
• Use the chat feature to either write a question
• r in the chat box, type “hand” and I will call
• n you soon thereafter or just shout out!
• Also, I’d love it if you kept your video on so I

can see you….

SLIDE 3

Today and especially Monday

• Covers some of the major results that resulted in the

awarding of the 2012 Nobel Prize in economics to Lloyd Shapley and Al Roth

• “The Prize concerns a central economic problem: how to

match different agents as well as possible. For example, students have to be matched with schools, and donors of human organs with patients in need of a transplant. How can such matching be accomplished as efficiently as possible? What methods are beneficial to what groups? The prize rewards two scholars who answered these questions

• n a journey from abstract theory on stable allocations to

practical design of market institutions.”

SLIDE 4

A basic definition

MECHANISM

An algorithm whose inputs come from agents with a strategic interest in the output. Each agent’s input is their own private information. Takes as input the reported preferences/data for a set of agents and produces as output an outcome, decision or action.

TODAY: MECHANISMS WITHOUT MONEY

Examples

anchors

voting

school chore

SLIDE 5

Office Allocation

• n people, n offices; each person has private preference
• rder over all offices.
• Mechanism for allocating offices to people?

One

sided matching problems

SLIDE 6

Algorithm 1

• People report preferences to algorithm.
• Algorithm visit students in alphabetical order and matches them to

their first choice if it’s available.

• Then, for all unmatched students, the algorithm visits them in

alphabetical order and matches them to their second choice if available.

• And so on until everyone matched.

A

B

C

I

02

02

03 03 003

• l

SLIDE 7

Pareto Optimality

• An outcome is Pareto optimal if you cannot make anyone

better off without also making someone else worse off.

SLIDE 8

Lemma: Algorithm 1 is Pareto optimal

• People report preferences to algorithm.
• Algorithm visit students in alphabetical order and

matches them to their first choice if it’s available.

• For all unmatched students, the algorithm visits

them in alphabetical order and matches them to their second choice if available.

• And so on until everyone matched.

i

get

their jthchoice

i

lowest

index

sit

b

some

person p

c Si

is

µ

strictly happier

in

M

p

is

matched to

• ffice allocated to

saypl

in M

in

round

Se

lei

1

• r visited earlies

p

is

worse

• ff

in round i

IIE

SLIDE 9

Is it truthful?

• That is, is it in each agents to report their

preferences truthfully?

Not

truthful

ABI

• l
• l
• l

2

03

03

03

03

SLIDE 10

Truthful mechanisms

• A mechanism is truthful or strategyproof or

dominant strategy incentive-compative (DSIC) if honesty is always the best policy.

• That is, no matter what other agents do, lying about

your preferences cannot make you better off.

ble

SLIDE 11

Algorithm 2: Serial dictatorship

• Pick an arbitrary ordering of the students.
• Visit the students in this order and let them pick their favorite available
• ffice that has not yet been picked.
• Pareto optimal?
• Truthful?

alphabetical

• l
• f
• 2

03

03

• I

SLIDE 12

Lemma: Serial Dictatorship is Pareto optimal

• Pick an arbitrary ordering of the students.
• Visit the students in this order and let them pick

their favorite available office that has not yet been picked.

Pfaff

mbeauocatan Consider first person

who

gets

different

alloc

in M

than

in M

M

SLIDE 13

Lemma: Serial Dictatorship is truthful

• Pick an arbitrary ordering of the students.
• Visit the students in this order and let them pick

their favorite available office that has not yet been picked.

Pick

personp

Fix

reports of

everyone

else

p

has

no incentive to lie

SLIDE 14

Why should we care about truthfulness?

difficult to

reason

abentontone

easier

• n agents

SLIDE 15

Office allocation

• n people (agents), each starts with an office
• Each person has a total order over all the offices.
• How should we reallocate them to get to a better allocation?

Top Trading Cycle

Algorithm

MTA

while

agents

remain

initially all

each remaining agent

to point

to

their

favorite

• ffice

claim

3 always cycle

in

resulting

directed graph

reallocate according to

that cycle

remove

all

those agents

repeat

b

ho agents

remain

SLIDE 16

C

SLIDE 17

Theorem: TTCA is a truthful mechanism

PI

Fox reports ofeveryone

but i

Suppose

that

if

i truthful

Ci

Ca CK

and

i

is

allocated

in

cycle

Cj

Claim

all

the

people in

G

n Cj

i

HM

their

allocation

to

any office

in

Cj

Ga

this

means

that

can

not

be

any cycle that

contains

i

any agent

in

C

Cj 1

i

can only

get

someone

in

Cg

n

G

getting

his

favorite by reporting truffles

D8

SLIDE 18

Theorem: The allocation produced by TTCA is stable

• The allocation is stable if no subset of agents could have

done better by not participating, but rather just reallocating amongst themselves.

all do atleast

aswell

at

fetishism

Proof by

Tuppose

there

is

asubset

A of agents that

prefer

to gooff reallocate

among themselves

Let

A'EA

be agents

in

A

thot get

a different

alloc

from

what

they would

havegotten

Iet Cj

be

first cycle

in

MTA

centering

a c A

C

g

get the

exact

same

allocah

So

a

has to

be dong strictly worse

D8

SLIDE 19

Pareto Optimality

• An outcome is Pareto optimal if in any other outcome at

least one agent is worse off.

• Is the outcome produced by TTCA Pareto optimal?

SLIDE 20

Kidney Exchange

Next set of slides created by Jason Hartline and Nicole Immorlica

SLIDE 21

Kidney failure Sometimes people find themselves without a kidney.

Diabetes Hypovolemia Dehydration Sepsis Rhabdomyolysis High blood pressure

Without a transplant, they will die.

SLIDE 22

Kidney supply

• 1. Cadavers

SLIDE 23

Kidney supply

• 2. Live donors

SLIDE 24

In 2008,

10,526 patients

received cadaver kidneys.

4,857 patients

received live donor kidneys.

SLIDE 25

Kidney demand

There are currently waiting for a kidney transplant in the US.

93,000 people

http://optn.transplant.hrsa.gov

SLIDE 26

In 2014,

Over 8,000 patients died

waiting or became too sick for a transplant.

SLIDE 27

Making supply meet demand

The economic approach 101: Buying kidneys.

I have an extra kidney. I need a kidney. My value for it is my value for my life.

SLIDE 28

Repugnance Often x + $ is repugnant, even when x alone is not. Interest on loans Prostitution Organ donation

SLIDE 29

“We didn’t have time to pick up a bottle of wine, but this is what we would have spent.”

SLIDE 30

Legality

Section 301 of the National Organ Transplant Act, “Prohibition of organ purchases” imposes criminal penalties on any person who

“knowingly acquire[s], receive[s], or

• therwise transfer[s] any human
• rgan for valuable consideration for

use in human transplantation”

SLIDE 31

Making supply meet demand

Take two:

Kidney exchange.

SLIDE 32

Compatibility

Blood “O”, “A”, “B”, “AB” Tissue (crossmatch test)

AM

SLIDE 33

Kidney exchange

Sick, blood type A Sick, blood type B Healthy, blood type A Healthy, blood type B

SLIDE 34

Have bunch of patient donorpairs

PED Biba

in Dn

Ideaifff

Use

MTA

agenty

• fay

patient

Y donor

total ordering each Pi hairy total

• n offices
• ver over

donorkidney

• rder of prob
• ftransplant

success

To

run

TTCA P D

y

can

extend

TTCA

f

J

BD

to

deal

patients

wo

donors

g

donors way patient

P3D

SLIDE 35

Issue

I

P D F

aD2

rye

4 surgeries

issue y

doing

sequentially

D

P

first

Da

can now renege

can't

legally

coerce

12 to follow thru

always

done simultaneously

don't

want

to

de long cycles

SLIDE 36

Issue

2

model is

• verall

Qi

is Hughley likely to work

• r not

transplant

input

to problem

G

Vp Ep

PEEL

• bjective

L9P

a

Ifk

Max cardilaty

matching

Input

reported to

National

kidney exchag

patientsHooton

want to

be

sure

incentivized to report

all edges

SLIDE 37

Essential

requirement

• leghas

to ensue

that

no patient

can

switch

frm

matched

to

unmanned

wedgesthey report

SLIDE 38