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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 the
New Business
Decision Tree
C:1
Red
1/2
1:1
Raise
2:1
Meet
2 -2
Pass
1 -1
Fold
1 -1
Black
1/2
1:2
Raise
2:1
Meet
-2 2
Pass
1 -1
Fold
-1 1
C:1
Red
1/2
1:1
Raise
2:1
Meet
2 -2
Pass
1 -1
Fold
1 -1
Black
1/2
1:2
Raise
2:1
Meet
-2 2
Pass
1 -1
Fold
-1 1
C:1
Red
1/2
1:1
Raise
2:1
Meet
2 -2
Pass
1 -1
Fold
1 -1
Black
1/2
1:2
Raise
2:1
Meet
-2 2
Pass
1 -1
Fold
-1 1
C:1
Red
1/2
1:1
Raise
2:1
Meet
2 -2
Pass
1 -1
Fold
1 -1
Black
1/2
1:2
Raise
2:1
Meet
-2 2
Pass
1 -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
credible
incredible
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
AliceBob
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 Peaches
Peaches
Pay
Balancing Act
PeachesLemons Peaches
Peaches
Pay
Balancing Act
Peaches
Lemons
Peaches
Peaches
Pay
Balancing Act
PeachesLemons Peaches
Pay
Balancing Act
PeachesLemons Peaches
Pay
Lemons
Balancing Act
Pay
Peaches
Lemons
Peaches
Lemons
Balancing Act
PeachesLemons Peaches
Pay
Lemons
Grim Trigger
This is going to be
our last project...
Alice
Betrays
Alice
Co-operates
Bob
Betrays 5,5 0,5
Bob
Co-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 University
James 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

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