Games People Play Economics 327 – Professor Chris Ellis

Games People PlayGames People Play

Economics 327 – Professor Chris EllisEconomics 327 – Professor Chris Ellis

Games People Play.Games People Play.

Games People Play:Games People Play:Some Preliminary Questions.Some Preliminary Questions.

Question:Question: What is game theory? What is game theory?Answer: Answer: The analysis of strategic situations.The analysis of strategic situations.

Question:Question: And what is a strategic situation? And what is a strategic situation?Answer: Answer: When two or more players follow strategies (plans When two or more players follow strategies (plans of action) that effect each others payoffs (happiness, of action) that effect each others payoffs (happiness, money, status etc) we have a strategic situation.money, status etc) we have a strategic situation.

Question:Question: What can a course on game theory do for me? What can a course on game theory do for me?Answer:Answer: It will allow you to predict the likely outcome of It will allow you to predict the likely outcome of any strategic situation, and possibly tell you how to any strategic situation, and possibly tell you how to manipulate the outcome to your advantage.manipulate the outcome to your advantage.



Remark:Remark: Sure it will….give me an example. Sure it will….give me an example.Reply:Reply: Remember Cortez, the guy that conquered the Aztec empire. He Remember Cortez, the guy that conquered the Aztec empire. He used an understanding of game theory to achieve victory. On landing on the 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 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 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. response was to burn his boats, giving his troops no avenue of retreat. Remark:Remark: Cortez was a nutter!! Cortez was a nutter!!Reply:Reply: No, he understood game theory. After his action his troops knew they 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 had to fight to the death and the Aztecs knew it too. So the Aztecs ran away.away.Remark:Remark: What What’’s that got to do with me and my degree?s that got to do with me and my degree?Reply: Reply: Well, the battle could be your efforts to get an A on this course, and 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 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.time off from studying so as to drink beer you might achieve your objective.Remark: Remark: I didn't know Cortez was an undergrad!!I didn't know Cortez was an undergrad!!Reply:Reply: Huh?!?! Huh?!?!




Games People PlayGames People PlaySyllabusSyllabus

Text:Text: Dixit and Skeath, Dixit and Skeath, ““Games of StrategyGames of Strategy”” 2 2ndnd Edition, Edition, Norton.Norton.Useful Reading:Useful Reading: Dixit and Nalebuff , Dixit and Nalebuff , ““Thinking Thinking Strategically: The Competitive Edge in Business and Strategically: The Competitive Edge in Business and Everyday LifeEveryday Life””, Norton., Norton.Tests:Tests: There will one midterm worth 25% and one final There will one midterm worth 25% and one final worth 50%. The remaining 25% will be earned via worth 50%. The remaining 25% will be earned via participation in in-class games.participation in in-class games.Exam Schedule:Exam Schedule:

Midterm Thursday October 31st

Final Thursday December 12th, 1.00pm.

Office Hours:Office Hours:Tuesdays and Thursdays 3.30-4.30 and by appointment.



The The ““Games of StrategyGames of Strategy”” strategy strategy1st edition - $35 (approximately)

2nd edition - $96.25 (from the Norton web site)

Your best strategy – buy used!!Your best strategy – buy used!!

Yes we can conclude Dixit and Skeath Yes we can conclude Dixit and Skeath ““wrote the bookwrote the book”” on games on games



Course OutlineCourse Outline1. Basic Ideas and Examples

Dixit and Skeath Chapter 1

2. How to Think About Strategic GamesDixit and Skeath Chapter 2

3. Sequential Move GamesDixit and Skeath Chapter 3

4. Simultaneous Move Games with Pure StrategiesDixit and Skeath Chapters 4 and 5

5. Mixed StrategiesDixit and Skeath Chapters 7 and 8

6. Combining Simultaneous and Sequential MovesDixit and Skeath Chapter 6

7. Uncertainty and InformationDixit and Skeath Chapter 9



Course Outline (continued)Course Outline (continued)

8. Strategic Moves Dixit and Skeath Chapter 10

9. The Prisoner’s Dilemma and Repeated GamesDixit and Skeath Chapter 11

10. Collective Action GamesDixit and Skeath Chapter 12

11. Evolutionary GamesDixit and Skeath Chapter 13

12. Brinksmanship: The Tragic Tale of George and SaddamDixit and Skeath Chapter 14

Auctions Dixit and Skeath Chapter 16

BargainingDixit and Skeath Chapter 17


When you see and hearWhen you see and hear

itit’’s time to play a game!!s time to play a game!!



The Name GameThe Name Game

Students should divide themselves into Students should divide themselves into groups of 5-8 individualsgroups of 5-8 individuals

Each group must select a crazy nameEach group must select a crazy name

The groups will then vote on which name The groups will then vote on which name is the craziestis the craziest

The group with the most votes winsThe group with the most votes wins


Real Minor League Baseball Team NamesReal Minor League Baseball Team NamesBoise Irrigators Union Boise Irrigators Union Cedertown Sea CowsCedertown Sea CowsCentralia ZerosCentralia Zeros Corsicana Gumbo BustersCorsicana Gumbo BustersDes Moines UndertakersDes Moines Undertakers Eau Claire PuffsEau Claire PuffsFreeport PretzelsFreeport Pretzels Fresno Raisin EatersFresno Raisin EatersHigh Point Furniture MakersHigh Point Furniture Makers Holyoke PaperweightsHolyoke PaperweightsHoquiam Perfect Gentlemen Hoquiam Perfect Gentlemen Ilion TypewritersIlion TypewritersIola GasbagsIola Gasbags Jackson Blind TigersJackson Blind TigersKalamazoo Celery EatersKalamazoo Celery Eaters Kirksville OsteopathsKirksville OsteopathsMayfield PantmakersMayfield Pantmakers Minot Why NotsMinot Why NotsMontpelier GoldfishMontpelier Goldfish Muncie Fruit JarsMuncie Fruit JarsNevada LunaticsNevada Lunatics Wilkesboro FlashersWilkesboro FlashersParis ParasitesParis Parasites Racine Malted MilksRacine Malted MilksRegina BonepilersRegina Bonepilers Springfield BabesSpringfield BabesTroy WasherwomenTroy Washerwomen Utica Pent-UpsUtica Pent-UpsVancouver Horse DoctorsVancouver Horse Doctors Waterloo LoonsWaterloo LoonsWaterloo MicrobesWaterloo Microbes Waycross BlowhardsWaycross BlowhardsZanesville Flood SufferersZanesville Flood Sufferers


1: Basic Ideas and Examples1: Basic Ideas and Examples

Classification of GamesClassification of GamesCooperative 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


Classification of GamesClassification of Games

The point of coming up with a classification of games is to allow us 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.to identify the precise nature of the situations we find ourselves in.

This is an essential first step to determining what strategies we This is an essential first step to determining what strategies we expect our opponents to follow, and what strategies are in our best expect our opponents to follow, and what strategies are in our best interests.interests.

Also if we identify that we are playing a game in which we are at a 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 disadvantage then we can attempt the change the game we are playing. playing.

Example: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!!



Cooperative or non-cooperativeCooperative or non-cooperativeAre 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.



Zero-sum or non-zero-sumZero-sum or non-zero-sumIn 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.



Full information or incomplete informationFull information or incomplete informationIn 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.



Sequential or simultaneousSequential or simultaneousIn 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.



One-shot or repeated or recurringOne-shot or repeated or recurringIs the game played once?

Repeatedly with the same opponent?

Repeatedly but with different opponents?



Fixed or Manipulable RulesFixed or Manipulable RulesIn 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



Enforceable or unenforceable agreementsEnforceable or unenforceable agreementsEnforceable 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


Terminology and DefinitionsTerminology and Definitions

PlayersPlayers

StrategiesStrategies

PayoffsPayoffs

RationalityRationality

Common knowledge of rulesCommon knowledge of rules

EquilibriumEquilibrium

Evolutionary gamesEvolutionary games

Experimental gamesExperimental games



Players.Players.– The players in a game are individuals, or groups of

individuals acting collectively (e.g. firms, government departments, countries etc.)



• StrategiesStrategies– 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.



• PayoffsPayoffs– What the players receive as the result of the various

possible outcomes of the game. These may be measured in dollars, happiness, prestige, or possiblygrades.grades.



• RationalityRationality– We assume that players follow their best strategies:

those that realize the highest expected payoff.



• Common knowledge of rulesCommon 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.



• EquilibriumEquilibrium– 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 The equilibrium of a game is what we expect and predict will happen.happen.



• Evolutionary gamesEvolutionary games– Some games are not based on the concept of

equilibrium. They are based on reactive learn-by-experience, and from observing others behavior. We then look for evolutionary stable states.



• Experimental gamesExperimental games– Games played under experimental conditions. In the

lab.– We shall play many such games.



The p-Beauty Contest GameThe p-Beauty Contest Game

• ObjectiveObjective– 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.



• BackgroundBackground– 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



• The equilibrium of this game is to choose zero!!The equilibrium of this game is to choose zero!!• Most people donMost people don’’t choose zerot choose zero

– Explanation #1:• A person might not be so clever, and only reasons one or

two levels deep into the iterated process.



– 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.



• Winning strategy: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.

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Games People Play Economics 327 – Professor Chris Ellis