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 ofquantum mechanics (1932)

Theory of Games and EconomicBehavior (1944)

"Stored program concept"

"Mutually assured destruction"and "Second strike capability"(Cold War)

-extravert

-extraordinary genius

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 notIf Y folds X wins one unitIf 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

Bet B

X wins 1

X

Y

Fold

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)

Nash Crowe

•1950: John Nash (equilibrium concept). Nobel prize for his work 1994, with Harsanyi and Selten.

THE basic example: PRISONER'S DILEMMA

silence confess

silence -1 , -1

-9 , 0

confess

0 , -9

-3 , -3

row

column

(0,-9) = ‘row’ gets 0, ‘column’ gets -9

Assumption

-simultaneous choice

-Complete information

-Single shot game

Prisoner's Dilemma: positive numbers

'cooperation’ ‘defection’

‘cooperation’ 3 , 3 0 , 5

‘defection’ 5 , 0 1 , 1

row

column

(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

(‘stay’) (‘swerve’)

(‘stay’) -50 , -50

20 , -10

(‘swerve’)-10 , 20

-5 , -5

row

column

“chicken game”:

it can be beneficial to restrict your options

Note: use arrows

The assurance game

cooperate defect

cooperate 60 , 60

10 , 50

defectie 50 , 10

20 , 20

row

column

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”

Boxing Ballet

Boxing 5 , 2

0 , 0

Ballet 0 , 0

2 , 5

man

woman

In coordination issues, game theory is not that useful

Tennis: mixed strategies

Anticipate backhand

Anticipate forehand

To backhand 60 , 40

90 , 10

To forehand80 , 20

40 , 60

Player 1

Player 2

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

Trust

No Trust

Honor trustAbuse Trust

(10, 10) (0, 80) (40, 40)

1

2

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)– …

QuestionHow 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)

THEORETICALLY1. The finitely repeated game2. The infinitely repeated game

THROUGH COMPUTER SIMULATIONSTit-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-very-attractive, 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 -2.0% to -15.0%“never bust” -6.0%mimic the dealer -5.7%basic strategy -0.5%basic strategy+ -0.0%card counting +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.

NOThe strong economyDemographyBetter policing strategies (Giuliani-New York)Gun control lawsCarrying concealed weapons lawsIncreased use of capital punishment

YESIncrease in the number of police officersRising prison populationReceding crack epidemicLegalizing 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

Visibility,

Feedback,

Awareness

DIY Kyoto

$$

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) 1592: 0.50$ 1013: Do us a favor and participate … 168

You get what you pay for, or not?

Drag the circle in the box as many times as possible

1: Chocolates (worth 5$) 1692: Snickers bar (worth 0.5$) 1623: Do us a favor and participate … 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 Patients are administered electro-shocks. They rate their pain level on a slider.

2 Patients were given Veladone (pain-killer, costs about $2.50 per dose).

3 Patients got same level electro-shocks again.

Pain decreased for almost all participants

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)