game theory for software developers at the boulder jug

Game Theoryfor Software Developers

by Matthew McCullough, Ambient Ideas, LLC

Matthew McCullough @matthewmccull

The Big Picture

4 Basic Elements

� Players� Strategies� Payoffs� Common knowledge

Games

Business

Economics

Game theory is...

Strategic interactive decision making

Strategy dependent on the choices of others

Economics as science

“Good fortune is what happens when opportunity meets with planning”

--Thomas Alva Edison

The Company

MacroCode

Consultancy

Underbid

Signaling

Stotting

Bid Low for the 1st Month

Build theNew Business

Decision Tree

C:1

Red

1/2 1:1

Raise

2:1

Meet2 -2

Pass1 -1

Fold1 -1

Black

1/2 1:2

Raise

2:1

Meet-2 2

Pass1 -1

Fold-1 1

C:1

Red

1/2 1:1

Raise

2:1

Meet2 -2

Pass1 -1

Fold1 -1

Black

1/2 1:2

Raise

2:1

Meet-2 2

Pass1 -1

Fold-1 1

C:1

Red

1/2 1:1

Raise

2:1

Meet2 -2

Pass1 -1

Fold1 -1

Black

1/2 1:2

Raise

2:1

Meet-2 2

Pass1 -1

Fold-1 1

C:1

Red

1/2 1:1

Raise

2:1

Meet2 -2

Pass1 -1

Fold1 -1

Black

1/2 1:2

Raise

2:1

Meet-2 2

Pass1 -1

Fold-1 1

Bounded Rationality

Beauty Contest

Beauty Contest Rules

� Guess between 1 and 100� Winner has the number at 70% of

the average guess

University Employees

The Red Button

The $2 Button: Rules� Gather 100 friends� Everyone starts with a $100 prize� Everyone gets a button� If you push, it deletes $2 from

everyone else's prize� Everyone gets one button push

appx. 30% push

Worried about retribution

The $2 Button: New Rules� Gather 100 random players� Everyone starts with a $100 prize� Everyone gets a button� If you push, it deletes $2 from

everyone else's prize� Everyone gets one button push� If you push, you cut your losses

in half

appx. 70% push

Framed as defense

Bilateral Anterior Insular Cortex

� What if everyone had a meet and greet in advance?

� What if everyone knew each other?� What if everyone was a family

member?

Red Button Coalitions?

Hiring

Incentives

Motivating others to do what we want them to with rewards

Aligning the other player's desires with ours

credibleincredible

vs

Big sale, 80% off for a limited time only!**

$20 per resume

$1000 if hired

One shot?

Iterative?

Rules

Don't push changes after Thursday

Don't disable your anti-virus software

Must have 100% test coverage

Unintended Consequences

� Some quantity of rules are what make a game playable

� Don't capriciously create new rules at the last moment

Scoring for the other Team� 1994: Barbados vs. Grenada� Must win by 2 goals to advance� B2:G1� Goals count double in overtime� Grenada began defending Barbados'

goal

Team Colors

Penny Altruism

Ultimatum Game

Ultimatum Game Rules

� The purse is provided by a bank� Players are not allowed to

communicate� There is only one decision to be

made� There are 100 strategies

Alice Bob

Bank

Ultimatum

Offer 100

Accept

100,0

Decline

0,0

Offer 99 Offer 98 Offer 30 Offer 10

Accept Decline Accept DeclineAccept DeclineAccept Decline

99,1 0,0 0,010,900,030,700,098,2

Alic

eBo

b

Fair

70/30 split

Observed

Commission

Between ages of 3 & 5

Anonymously

Offer: 1 to 10

No Way Back

Strategically removing options

Prisoner's Dilemma

Alice Defects Alice Stays Silent

Bob Defects -4,-4 0,-5

Bob Stays Silent -5,0 -1,-1

Dev Tests Dev Shirks

QA Tests -1,-1 -1,0

QA Shirks 0,-1 -2,-2

Testing

Centipede Game

100% Test Coverage

Monty Hall

Bayes Formula

Birthday Attack

� With 26 people in the room, what is the chance that someone has January 1st as their birthday?

Birthday Attack

� With 26 people in the room, what is the chance that any two share a birthday?

Retailer Selection

Red/Black Cards

Red/Black Negotiations

� 23 Red Cards with instructor� 23 Cards with students� What kind of deal do you hold out

for?

Alice loses three cards

Red/Black Negotiations

� 20 Red Cards with instructor� 23 Cards with students� What kind of deal do you hold out

for?

Acquisition

No!

Threat?

Commitment

Doomsday Device

Poison Pill

Brinksmanship

Chicken

What is it?

� Playing at high stakes� By not offering any small response,

scaring the other player of the consequences of the big response

Chicken

� Best way to play is to throw out the steering wheel

� But the other player must visibly take notice of that action

Partnerships

Incremental value

Shapley Value

Factory

Factory Sizes

� Small: $60,000� Medium: $90,000� Large: $130,000

Advertising

Warranty

Signaling

Quality

Lifetime

Google Adwords

Price

Thomas Schelling

Schelling points

Schelling Points� Grand Central Station in New York� 99¢ on the App Store� $39.95 for FPS games� DVD releases on Tuesday� Comic books releases on Wednesday� Theater film releases on Friday

How do they occur?

� Publicity � Competition� Frequency� Tradition

Google

Etsy

Schelling Number

Schelling Number

� Write down an two-digit odd number in which both the digits are different

Vendor Trouble

Late

Fire them?

We need 10 of 12

Lemons

George Akerlof

Balancing Act

PeachesLemons PeachesPeaches

Pay

Balancing Act

PeachesLemons PeachesPeaches

Pay

Balancing Act

Peaches

Lemons

PeachesPeaches

Pay

Balancing Act

PeachesLemons Peaches

Pay

Balancing Act

PeachesLemons Peaches

Pay

Lemons

Balancing Act

Pay

Peaches

LemonsPeaches

Lemons

Balancing Act

PeachesLemons Peaches

Pay

Lemons

Grim Trigger

This is going to be our last project...

AliceBetrays

AliceCo-operates

BobBetrays 5,5 0,5

BobCo-operates 5,0 1,1

make it sequential

Co-operate Co-operate Co-operate Co-operate Co-operate Co-operate Co-operate Co-operate

Co-operate Co-operate Co-operate Co-operate Co-operate Co-operate Co-operate Betray

Co-operate Co-operate Co-operate Co-operate Co-operate Co-operate Betray

Co-operate Co-operate Co-operate Co-operate Co-operate Betray

Co-operate Co-operate Co-operate Co-operate Betray

Co-operate Co-operate Co-operate Betray

Co-operate Co-operate Betray

Co-operate Betray

Betray

Simultaneous Shoe Bidding

What would you bid for this pair of shoes?

What would you bid if you only had a 50% chance of

getting the other shoe?

XKCD 601: Game Theory

Game Theoryfor Software Developers

by Matthew McCullough, Ambient Ideas, LLC

References: Software

� Gambit� http://www.gambit-project.org/doc/index.html� http://www.gambit-project.org/doc/samples.html

� Game Theory Explorer� http://gametheoryexplorer.appspot.com/builder/

References: Research

� The Teaching Company: Game Theory Video Course� http://www.thegreatcourses.com/tgc/courses/Course_Detail.aspx?cid=1426� Professor Scott P. Stevens, Ph.D.

The Pennsylvania State UniversityJames Madison University

� Bookmarks� http://www.delicious.com/matthew.mccullough/gametheory

� Range Voting� http://rangevoting.org/TBlecture.html

� Market for Lemons� http://en.wikipedia.org/wiki/Market_for_lemons� http://nobelprize.org/nobel_prizes/economics/laureates/2001/akerlof-article.html� http://www.springerlink.com/content/h3h8530156276515/� http://hydrogen.its.ucdavis.edu/eec/education/EEC-classes/eeclimate/class-

readings/akerlof-the%20market%20for%20lemons.pdf

References: Blogs

� Mind Your Decisions� http://mindyourdecisions.com/blog/

� Game Theory Strategies� http://www.gametheorystrategies.com/

� Twitter, Barry Hughes� https://twitter.com/#!/gamethry

References: Books

� Theory of Games and Economic Behavior� http://en.wikipedia.org/wiki/Theory_of_Games_and_Economic_Behavior� http://press.princeton.edu/titles/7802.html� http://www.amazon.com/Economic-Behavior-Commemorative-Princeton-Editions/

dp/0691130612/ref=sr_1_1?ie=UTF8&qid=1310015156&sr=8-1� Rock, Paper, Scissors: Game Theory in Everyday Life

� http://www.amazon.com/Rock-Paper-Scissors-Theory-Everyday/dp/0465009387/ref=sr_1_2?ie=UTF8&qid=1310490759&sr=8-2

� The Art of Strategy: A Game Theorist's Guide to Success in Business and Life� http://www.amazon.com/Art-Strategy-Theorists-Success-Business/dp/0393337170/

ref=pd_bxgy_b_text_c� Co-Opetition : A Revolution Mindset That Combines Competition and Cooperation :

The Game Theory Strategy That's Changing the Game of Business� http://www.amazon.com/Co-Opetition-Revolution-Combines-Competition-

Cooperation/dp/0385479506/ref=pd_sim_b_1

References: People

� John von Neumann� http://en.wikipedia.org/wiki/John_von_neumann

� Thomas Schelling� http://en.wikipedia.org/wiki/Thomas_Schelling

� John Forbes Nash� http://en.wikipedia.org/wiki/John_Forbes_Nash

� John Harsanyi� http://en.wikipedia.org/wiki/John_Harsanyi

Photo Credits� 100 Dollar Bill Roll

� http://www.flickr.com/photos/85473033@N00/3367543296� Pennies

� http://flic.kr/p/6ucLDE� http://flic.kr/p/6u8BEa

� Earth� http://flic.kr/p/9DTDXi

� Dice� http://flic.kr/p/9g1aZc

� Cards� http://flic.kr/p/4UwZc6� http://flic.kr/p/6FKnGu� http://flic.kr/p/4V67rx

� Happy Hour� http://www.flickr.com/photos/beleaveme/3276175127/

� Prison� http://flic.kr/p/38wBWq

Other Ideas

� Bounded Rationality� 2-3 event horizon

� Typing� Pooling or separating equilibria

� Prisoner's Dilemma with an Arbiter� Tragedy of the Commons

� Air pollution� Mass transit tickets� Overfishing

� Volunteer's Dilemma� Witnessing a crime