Judgment and decision making
Chris Snijders,
ETH, April 28-29
1. Two boxes (2x720 gr) of Belgium Godiva chocolates
27, 40, 70, 70, 10
2. This book on architecture
0, 0, 25, 60, 30
3. A wireless keyboard
20, 0, 90, 150, 10
4. A used 4 Gb Ipod Nano,
in excellent condition
70, 80, 50, 200, 80
5. A remote controlled toy helicopter
120, 25, 60, 30, 10
6. A bottle of red Italian Brunello wine
5, 40, 35, 30, 15
GAME THEORY
I know some of you have some knowledge about this
already, but any course in decision making would not be
complete without it.
We model life, and start with the game of poker
John von Neumann (1903-1957)
Hungarian
Göttingen (with Hilbert), Berlin,
Hamburg, Princeton.
The mathematical foundations of
quantum mechanics (1932)
Theory of Games and Economic
Behavior (1944)
-extravert
-extraordinary genius
"Stored program concept"
"Mutually assured destruction"
and "Second strike capability"
(Cold War)
Life  Poker  SimplePoker
Player X and Y receive a random number [0,1]
Ante: one unit
Player X first decides whether or not to bet a given amount,
B
If X bets, then Y decides to fold or not
If Y folds  X wins one unit
If Y calls  compare: highest number wins B+1
If X does not bet, then cards compared and highest wins 1
SimplePoker (von Neumann variation)
Highest wins 1
Fold
X
Fold
Bet B
X wins 1
Y
Call
Highest wins B
Optimal strategy in von Neumann's SimplePoker
• Player X's optimal strategy is of the form:
"Bet" if (number < a) or (number > b)
for some 0<a<b<1
• Player Y's optimal strategy is of the form:
"Call" if number > c for some c, 0<a<c<b<1
It appears that the numbers a, b and c equal
NOTE:
bluffing is part of the
optimal strategy! But
do it with your worst
hands.
So this game theory thing might work ...
• Chris Ferguson (1963 - ...)
• UCLA, Computer Science (mother
doctoral degree in math, father
teaches game theory at UCLA)
• Became acquainted with the work on
poker by von Neumann and others,
and extended it to real-life poker
• Beat TJ Cloutier in 2000 using
(largely) a mathematical strategy
• Has won many major tournaments
since
• Now has his own poker-site
(Full Tilt Poker)
Chris "Jesus" Ferguson
Game theory: Some history
• Started with Von Neumann and Morgenstern (1944:
Theory of games and economic behavior)
•1950: John Nash (equilibrium concept). Nobel
prize for his work 1994, with Harsanyi and
Selten.
Nash
Crowe
THE basic example: PRISONER'S DILEMMA
Assumption
column
-simultaneous
choice
silence
confess
silence
-1 , -1
-9 , 0
confess
0 , -9
-3 , -3
-Complete
information
-Single shot
game
row
(0,-9) = ‘row’ gets 0, ‘column’ gets -9
Prisoner's Dilemma: positive numbers
column
'cooperation’
‘cooperation’
row
‘defection’
‘defection’
3,3
0,5
5,0
1,1
(30,0) = ‘row’ gets 30, ‘column’ gets 0
What will people do in this simple game?
• Assumptions:
– Players have selfish goals ...
– ... and try to achieve those goals in a consistent
(=rational) manner
• Under these circumstances, the prediction is
that rational egoists will choose for defection.
• Why would that be?
Some game theortic lingo
• A game as you saw it, is a game in "normal form" (as
opposed to "extensive form")
• A strategy is a rule that prescribes how an actor will
behave in all possible situations that can arise in a game.
• A strategy is dominant for actor i if this strategy delivers
more than his other strategies, irrespective of what
other players choose
• A combination of strategies is a Nash-equilibrium (or
just: equilibrium) if – given the strategy choices of
others – no actor has an incentive to deviate his or her
strategy unilaterally
How this works out in the Prisoner's Dilemma
• Strategy = cooperation or defection
• Defection is a dominant strategy, because
whatever strategy the other party chooses,
defection has a higher payoff.
• And: the strategy combination:
(defection, defection) is in equilibrium. Neither
of the two players has an incentive to deviate if
the other stays put. NOTE: they have an
incentive to deviate both, but this does not
count.
Game Theory's prediction(s)
• People will end up in strategy combinations
that are in equilibrium (and will tend to use
dominant strategies)
•  Whenever there is just a single equilibrium,
then that is the game-theoretic prediction.
•  Whenever there are more, then still unclear
which of these it is going to be
The Prisoner's Dilemma paradox
• Rational egoists end up in (defection,
defection). This is a Pareto-inferior result.
• Games where individually rational behavior
leads to an outcome that is collectively
irrational are called social dilemmas.
• Hence: the Prisoner's Dilemma is a social
dilemma.
GAME THEORY: example games
“chicken game”:
it can be beneficial to restrict your options
column
(‘stay’)
(‘stay’)
(‘swerve’)
-50 , -50
20 , -10
-10 , 20
-5 , -5
row
(‘swerve’)
Note: use
arrows
The assurance game
column
cooperate
defect
cooperate
60 , 60
10 , 50
defectie
50 , 10
20 , 20
row
Two equilibria in pure strategies, one is Pareto-optimal, one
is not. In all likelihood people will choose the one that is
Pareto-optimal.
“The battle of the sexes”
woman
Boxing
Ballet
Boxing
5,2
0,0
Ballet
0,0
2,5
man
In coordination issues, game theory is not that useful
Tennis: mixed strategies
Player 2
Anticipate
backhand
Anticipate
forehand
To backhand
60 , 40
90 , 10
To forehand
80 , 20
40 , 60
Player 1
NB1 A so-called "zero-sum" game.
NB2 Equilibria?
The Nash existence theorem (Nash, 1950)
• In a game with n players, and each players with a finite
number of strategies, you will find at least one
equilibrium, possibly in mixed strategies.
• A mixed strategy is a probability distribution over the
different strategies.
For instance (prev. slide): serve to forehand in 40% of
the cases, to backhand in 60% of the cases.
• NB The number of equilibria is always odd (2n+1)!
Tennis example: mixed strategies
Anticipate
backhand
q
Anticipate
forehand
1-q
To
backhand
p
60 , 40
90 , 10
To
forehand
1-p
80 , 20
40 , 60
You find out:
Behavior of the one serving is
dependent on payoffs of the one
receiving!
Look at the one receiving the service.
When anticipating backhand
:
40 p + 20 (1-p) = 20 + 20 p
When anticipating forehand
:
10 p + 60 (1-p) = 60 - 50 p
In equilibrium, these two have to be equal (THINK!) 
In equilibrium : p = 4/7 = 0,57 . Similarly, you can calculate q in
equilibrium.
You saw different forms before: Trust Game
In extensive form. Example: Trust Game
1
Trust
No Trust
2
Abuse Trust
(10, 10)
(0, 80)
Honor trust
(40, 40)
Other (representations of) games: auctions
• Using text and formulas:
“Second-price auctions” or “Vickrey
auctions”
There are n bidders in an auction who each
bid once, in secret (closed), to the seller.
The one with the highest bid gets the object,
but pays only the second highest bid.
Show that “just bidding what the product is worth
to you” is a Nash-equilibrium.
Note: that bidding is closed, and not outloud,
makes a big difference.
What is the problem with "standard" auctions,
where you pay the price you bid (if you win)?
Collective goods: n-person PDs
• The issue is that the costs are personal, but the benefits
accrue to everybody  “Free riders behavior”
Real life examples
– Environmentally friendly behavior (vs not)
- Over-fishing, global warming, etc
- Tax evasion
– Arms race
– Cleaning joint property (such as a kitchen)
– Cooperation between firms (patents, firms)
– …
Question
How can be solve these kinds of free-rider problems?
"Solutions" to the single-shot PD
Three types of solutions:
- sanctions
- norms
- repetition
The point is not that these are huge insights, but that
they can be shown to help in the PD context
Solution 1: norms
A "mental bonus"
shifts the
equilibrium away
from mutual
defection.
Solution 2: repetition
“The evolution of cooperation” (1984)
THEORETICALLY
1. The finitely repeated game
2. The infinitely repeated game
THROUGH COMPUTER SIMULATIONS
Tit-for-tat: "I will be nice as long as you are"
Repetition can work: The Trench warfare
Miscellaneous
interesting stuff
What the following examples have in common (perhaps)
• Challenge your intuitions; let choices speak
Check what people do, and you can infer their
preferences. This might show what you thought
all along, but that need not be
• Experiment: it's a starting science To affect
behavior "standard judgment and decision
making knowledge" is not readily available.
You need some experimenting to see what
works.
• It's subtle. Small things might affect what
people actually do.
JDM – relations: let your choices speak
The art of internet-dating
[Hortacsu, Hitsh & Ariely]
looked at internet dating of
30,000 American users.
It seems the creme-de-la-creme is out there!
- earn more money than average
- are taller than average
- 70% has above average looks
- 28% of women are blond (way above average)
Add a photo!
A low-income, poorly educated, unhappily employed, not-veryattractive, slightly overweight, and balding man with photo
gets as much email as a rich and handsome guy who did not
post a photo.
JDM: relations (2)
The art of internet-dating: boy-girl differences
Men do better when they state they want a relationship, women do better when
they state they don’t.
Richer men get more replies. For women there is an increase first but a decrease
later. Having a college degree helps.
Women date: policemen, firemen, lawyers, financial executives, but not laborers,
actors, students.
Men date: students, artists, musicians, but not secretaries, military/policewomen.
Men: being short is a disadvantage, so is red or curly hair, or baldness.
Women: be blond! Blond hair has about the same value as a college degree.
JDM: blackjack
The only game played against the house in a casino in
which you can have a positive expectation is blackjack.
Some standard strategies (estimated)
typical casino player
“never bust”
mimic the dealer
basic strategy
basic strategy+
card counting
-2.0% to -15.0%
-6.0%
-5.7%
-0.5%
-0.0%
+1.5% to +2.5%
Ed Thorp “Beat the dealer” (1962)
JDM: blackjack (2)
BLACKJACK BASIC STRATEGY
JDM: blackjack (3)
Why making a living out of black-jack is unlikely
Gain: 1.5%
- You play about 100 hands per hour (if you're lucky)
- With a betting spread of 1 – 20 units, you bet about 400
units per hour
- With an edge of 1.5%, you win 6 unit per hour
- For a 120$ per hour wage, you need units of 20$
- For this, you need a bankroll that can take frequent hits
of 4,000$.
- If you have that, you need not play Black Jack all day
JDM: Lying
“It’s written all over your face.”
People tend to think that they can tell when somebody’s lying.
Typically, we can’t (average success rate: 55%). It seems that a really
small percentage of people is really good at it (around 70%).
Try
http://www.sciencenews.org/articles/20040731/bob8.asp
In other areas, reading a person’s face has been successfully applied.
See the research by Gottman about marriage success.
JDM: crime rates [how policy can affect criminal
behavior, indirectly]
Four reasons why crime rates went down in the 1990s in the US, and six reasons
that sound ok but are actually not related.
NO
YES
The strong economy
Demography
Better policing strategies (Giuliani-New York)
Gun control laws
Carrying concealed weapons laws
Increased use of capital punishment
Increase in the number of police officers
Rising prison population
Receding crack epidemic
Legalizing abortion
[Levitt, S. (2004) Understanding Why Crime Fell in the 1990s: Four Factors that Explain the Decline and Six that Do Not. Journal of
economic perspectives, 18,1: 163-190.]
•
•
•
•
•
•
iNcentives
Understand mappings
Defaults
Give feedback
Expect error
Structure complex choice
("a little push")
Subtle things matter in JDM
(cf. Thaler & Sunstein, 2008)
Applying JDM implies experimenting
"Prince de Lignac" beats the marketeers
1980: 0,5 - 2 miljard HFL
DIY Kyoto
Visibility,
Feedback,
Awareness
Example nudges
$$
$$
You get what you pay for, or not?
Drag the circle in the box as many times as possible
1: 5$ (5 minutes)
2: 0.50$
3: Do us a favor and participate …
159
101
168
You get what you pay for, or not?
Drag the circle in the box as many times as possible
1: Chocolates (worth 5$)
2: Snickers bar (worth 0.5$)
3: Do us a favor and participate …
169
162
168
You get what you pay for, or not?
Drag the circle in the box as many times as possible
1: A 5 dollar chocolate box
2: A 50 cents Snickers bar
?
101
The same goes for parents …
(source: Ariely)
Priming your suspect …
Rearrange:
aggressive make other to and it is rude to
disrespectful gestures drivers
Or:
future can gentle beneficial people who are and kind
expect a
Ask people to hand over their results …
[you get 5 vs 9 minutes]
(source: Ariely)
Priming your suspect (2) …
Rearrange:
embrace life like outgoing youngsters fast to move
and sporty
Or:
Florida pension change slow senior citizens in slowly
their plans
Measure the time they take to cross the hallway
[the red group is much slower!]
(source: Ariely)
Priming (3)
• Students do a task where cheating is possible (such
as grade their own tests)
• Three “before” conditions:
– Control
– Students wrote down 10 books they had read
– Students wrote down the 10 commandments
The Veladone study
1
3
Patients are administered electro-shocks. They rate
their pain level on a slider.
Patients were given Veladone (pain-killer, costs
about $2.50 per dose).
Patients got same level electro-shocks again.

Pain decreased for almost all participants
2
However: only half of the participants experienced a
decrease in pain when the drug was only 10 cents!
(source: Ariely)
The assignment
• Email your assignment no later than
May 23
• to c.c.p.snijders@gmail.com
See the online instructions for what the assignment
should be.
Stay in touch if anything is unclear.
(6 – perfect, 5 – good, 4 – pass, 3: don't)