Games People Play
Economics 327 – Professor Chris Ellis
Games People Play:
Some Preliminary Questions.
Question: What is game theory?
Answer: The analysis of strategic situations.
Question: And what is a strategic situation?
Answer: When two or more players follow strategies (plans
of action) that effect each others payoffs (happiness,
money, status etc) we have a strategic situation.
Question: What can a course on game theory do for me?
Answer: It will allow you to predict the likely outcome of
any strategic situation, and possibly tell you how to
manipulate the outcome to your advantage.
Games People Play.
Games People Play
Remark: Sure it will….give me an example.
Reply: Remember Cortez, the guy that conquered the Aztec empire. He
used an understanding of game theory to achieve victory. On landing on the
shores of Mexico he found that he and his conquistadors were outnumbered
hundreds to one by a waiting Aztec army. Faced by these odds his
response was to burn his boats, giving his troops no avenue of retreat.
Remark: Cortez was a nutter!!
Reply: No, he understood game theory. After his action his troops knew
they had to fight to the death and the Aztecs knew it too. So the Aztecs ran
away.
Remark: What’s that got to do with me and my degree?
Reply: Well, the battle could be your efforts to get an A on this course, and
you are Cortez. If you can find a way of denying yourself the ability to take
time off from studying so as to drink beer you might achieve your objective.
Remark: I didn't know Cortez was an undergrad!!
Reply: Huh?!?!
Games People Play.
Games People Play
Games People Play.
Games People Play
Syllabus
Text: Dixit and Skeath, “Games of Strategy” 2nd Edition,
Norton.
Useful Reading: Dixit and Nalebuff , “Thinking
Strategically: The Competitive Edge in Business and
Everyday Life”, Norton.
Tests: There will one midterm worth 25% and one final
worth 50%. The remaining 25% will be earned via
participation in in-class games.
Exam Schedule:
Midterm Thursday October 31st
Final Thursday December 12th, 1.00pm.
Office Hours:
Tuesdays and Thursdays 3.30-4.30 and by appointment.
Games People Play.
Games People Play
The “Games of Strategy” strategy
1st edition - $35 (approximately)
2nd edition - $96.25 (from the Norton web site)
Your best strategy – buy used!!
Yes we can conclude Dixit and Skeath
“wrote the book” on games
Games People Play.
Games People Play
Course Outline
1.
Basic Ideas and Examples
Dixit and Skeath Chapter 1
2.
How to Think About Strategic Games
Dixit and Skeath Chapter 2
3.
Sequential Move Games
Dixit and Skeath Chapter 3
4.
Simultaneous Move Games with Pure Strategies
Dixit and Skeath Chapters 4 and 5
5.
Mixed Strategies
Dixit and Skeath Chapters 7 and 8
6.
Combining Simultaneous and Sequential Moves
Dixit and Skeath Chapter 6
7.
Uncertainty and Information
Dixit and Skeath Chapter 9
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Games People Play
Course Outline (continued)
8.
Strategic Moves
Dixit and Skeath Chapter 10
9.
The Prisoner’s Dilemma and Repeated Games
Dixit and Skeath Chapter 11
10. Collective Action Games
Dixit and Skeath Chapter 12
11. Evolutionary Games
Dixit and Skeath Chapter 13
12. Brinksmanship: The Tragic Tale of George and Saddam
Dixit and Skeath Chapter 14
13. Auctions
Dixit and Skeath Chapter 16
14. Bargaining
Dixit and Skeath Chapter 17
Games People Play.
When you see and hear
it’s time to play a game!!
Games People Play.
Games People Play.
The Name Game
Students should divide themselves into
groups of 5-8 individuals
Each group must select a crazy name
The groups will then vote on which name
is the craziest
The group with the most votes wins
Games People Play.
Real Minor League Baseball Team Names
Boise Irrigators Union
Centralia Zeros
Des Moines Undertakers
Freeport Pretzels
High Point Furniture Makers
Hoquiam Perfect Gentlemen
Iola Gasbags
Kalamazoo Celery Eaters
Mayfield Pantmakers
Montpelier Goldfish
Nevada Lunatics
Paris Parasites
Regina Bonepilers
Troy Washerwomen
Vancouver Horse Doctors
Waterloo Microbes
Zanesville Flood Sufferers
Cedertown Sea Cows
Corsicana Gumbo Busters
Eau Claire Puffs
Fresno Raisin Eaters
Holyoke Paperweights
Ilion Typewriters
Jackson Blind Tigers
Kirksville Osteopaths
Minot Why Nots
Muncie Fruit Jars
Wilkesboro Flashers
Racine Malted Milks
Springfield Babes
Utica Pent-Ups
Waterloo Loons
Waycross Blowhards
Games People Play.
1: Basic Ideas and Examples
Classification of Games
Cooperative or non-cooperative
Zero-sum or non-zero-sum
Full information or incomplete information
Sequential or simultaneous
One-shot or repeated or recurring
Fixed or manipulable rules
Enforceable or unenforceable agreements
Games People Play.
Classification of Games
The point of coming up with a classification of games is to allow us
to identify the precise nature of the situations we find ourselves in.
This is an essential first step to determining what strategies we
expect our opponents to follow, and what strategies are in our best
interests.
Also if we identify that we are playing a game in which we are at a
disadvantage then we can attempt the change the game we are
playing.
Example: A firm is engaged in bargaining over the price of an input.
They find they have a very weak position. One possibility is not to
bargain. Instead put a supply contract out for tenders!!
Games People Play.
Classification of Games
Cooperative or non-cooperative
Are the players interests in conflict or not?
In cooperative games the players interests are aligned.
In non-cooperative games their interests are either
partially or totally in conflict.
Games People Play.
Classification of Games
Zero-sum or non-zero-sum
In a zero sum game one players gain is precisely the other
players loss.
A coin flip is a zero sum game.
A non-zero-sum game has the property that whatever is to be
divided between the players changes with the actions they take.
Games People Play.
Classification of Games
Full information or incomplete information
In a full information game all players know
everything about the game.
In an incomplete information game the value to the
other player of the outcomes of the game is
imperfectly known.
Games People Play.
Classification of Games
Sequential or simultaneous
In a sequential game the players take it in turns to
move.
Example: Chess is a sequential game.
In a simultaneous game all players move at the
same time.
Example: Rock-Paper-Scissors.
Games People Play.
Classification of Games
One-shot or repeated or recurring
Is the game played once?
Repeatedly with the same opponent?
Repeatedly but with different opponents?
Games People Play.
Classification of Games
Fixed or Manipulable Rules
In a fixed rule game the rules are given
Example: Chess
In a manipulable rule game the rules are determined
by pre-play
Example: Setting a legislative agenda
Games People Play.
Classification of Games
Enforceable or unenforceable agreements
Enforceable agreements can be determined and
enforced via sanctions stipulated in the contract
Example: A contractor often has to pay a penalty if a job is
not completed on time
Unenforceable agreements
Example: The promise of aid from one sovereign nation to
another
Games People Play.
Terminology and Definitions
Players
Strategies
Payoffs
Rationality
Common knowledge of rules
Equilibrium
Evolutionary games
Experimental games
Games People Play.
Terminology and Definitions
Players.
The players in a game are individuals, or groups of
individuals acting collectively (e.g. firms, government
departments, countries etc.)
Games People Play.
Terminology and Definitions
Strategies
The choices available to the players. If the game is
sequential then strategy refers to the players plans,
and may involve rules like:
If he plays A then I will play B, otherwise I will play C.
Games People Play.
Terminology and Definitions
Payoffs
What the players receive as the result of the various
possible outcomes of the game. These may be
measured in dollars, happiness, prestige, or possibly
grades.
Games People Play.
Terminology and Definitions
Rationality
We assume that players follow their best strategies:
those that realize the highest expected payoff.
Games People Play.
Terminology and Definitions
Common knowledge of rules
We assume that the players have a common
understanding of the rules of the game.
This does not mean that we cannot allow for
surprises or unforeseen circumstances.
These are possibilities to which a very small
probability is attached.
Hence this assumption is not restrictive at all.
Games People Play.
Terminology and Definitions
Equilibrium
This is the result of the game.
When each player has made all their rational moves
and neither wants to change, then we have found the
solution.
This is the definition of an equilibrium.
The equilibrium of a game is what we expect and predict
will happen.
Games People Play.
Terminology and Definitions
Evolutionary games
Some games are not based on the concept of
equilibrium. They are based on reactive learn-byexperience, and from observing others behavior. We
then look for evolutionary stable states.
Games People Play.
Terminology and Definitions
Experimental games
Games played under experimental conditions. In the
lab.
We shall play many such games.
Games People Play.
Games People Play.
The p-Beauty Contest Game
Objective
Choose a number between 0 and 100. If the
number you choose is the closest to 2/3 of the
average of all the other players choices, you win.
Games People Play.
The p-Beauty Contest Game
Background
A beauty contest game because it bears strong
resemblance to newspaper beauty contests discussed by
John Maynard Keynes (famous English economist) 60
years ago
A collection of women's faces printed in the newspaper
The object: To pick those that would be rated "prettiest.“
The strategy:
One should not vote for the faces he or she truly thought were
prettiest
or even the ones he or she thought most people would think were
prettiest
but the ones that one thought most people would think that most
people would think were the prettiest, and so on
Games People Play.
The p-Beauty Contest Game
The equilibrium of this game is to choose zero!!
Most people don’t choose zero
Explanation #1:
A person might not be so clever, and only reasons one or
two levels deep into the iterated process.
Games People Play.
The p-Beauty Contest Game
Explanation #2
A person fully realizes 0 is the equilibrium of the game but
does not believe that other players are equally clever.
Because a player did not pick 0, we cannot infer that the
player is irrational. It can only be inferred that rationality
is not common knowledge. After all, a person who
selected 0 would not win.
Without common knowledge, any number selected below
75 can be justified. In other words, a rational person can
pick a number greater than zero, but only if she believes
some in the group to be irrational.
Games People Play.
The p-Beauty Contest Game
Winning strategy:
To win the p-beauty contest, you have to be just
one step smarter than the average person, but not
too clever.
If you are too clever, you will select a number too
low.
Think of a seller in the stock market. He wants to sell
his shares just before the average person is selling,
when the price of the share is at its peak. Therefore, he
does not want to sell it too early.
Games People Play.