978-0393919684 Chapter 1 Lecture Note Chapter 1 & 2 Part 2

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GAME 4—The Tire Story (The Pure Coordination Game)

Another game that we have successfully played in the first lecture is based on the “We

can’t take the exam; we had a flat tire” story from Section 2 of Chapter 1. Even if the students

have read ahead, the discussion in the text makes it clear that there is no obvious focal answer to

the question, “Which tire?”

Bring along a stack of index cards and, when you are ready to play this game, hand one

card to each student. After relating the story, ask each student to pretend that she is one of those

taking the exam and must answer the tire question on the card. Collect the cards and tabulate the

answers on the board. Start a discussion about why different students chose different tires; focus

on the difficulties of obtaining a focal equilibrium when players have different backgrounds or

concerns. You can also relate the discussion back to the material in the text regarding the

necessity of being prepared to face a strategically savvy opponent at any time.

GAME 5—Single-Offer Bargaining (The Ultimatum Game)

Two players, A and B, are chosen. Player A offers a split of a dollar (whole dimes only).

If B agrees, both get paid the agreed coins and the game is over. If B refuses, it is B’s turn, but

now the sum is only 80 cents. If A accepts B’s offer, the two get paid the agreed coins. If A

refuses, the game is over and neither gets anything.

Do this five times in succession with different pairs and the second-round totals falling

successively to 70, 60, 50, and 40 cents. Keep a record of the successive outcomes.

Again hold a brief discussion. The aim is to get students to start thinking about rollback

and subgame perfectness and, if students understand these strategies but still don’t play them,

why they don’t. Also, consider how the discrepancy changes with the second-round fraction.

GAME 6—Divide a Dollar

This game asks pairs of students (or each student individually, if you use a handout and

match students with a random opponent after the fact) to divide a dollar between them. Each

writes the amount of the dollar he wants—1 cent or $1 or some value in between. If the amounts

requested for a given pair of students (or for two randomly selected student responses) add up to

$1 exactly, then each student gets the amount requested. If the two amounts add up to anything

other than $1, each player gets nothing. You can play this with real money if you can afford it; we

have managed to play this particular game without actual cash with perfectly acceptable results.

In actual play this is a game with discrete strategies, 100 for each player, or fewer if the

choices are restricted to be multiples of nickels or dimes or even quarters. Thus, it is also relevant

to (and discussed again in) Chapter 4. But you may prefer to conduct an analysis of the game,

treating the choices as continuous variables, in which case the game could be placed in Chapter 5.

Discussion of the game will bring out the idea that a game can have multiple equilibria

(any two values summing to $1 can make up an equilibrium) but that sometimes one of those

multiple equilibria is focal. This game is in direct contrast, then, with the tire game described in

Game 4 in which there are also multiple equilibria but none are as obviously focal as 50 cents

each is here. You can consider the various types of games in which multiple equilibria arise,

including an assurance-type game, Battle of the Two Sexes, and Chicken (Chapter 4). In some

cases, there are focal outcomes; in others, players may prefer to alternate among the different

equilibria. You can lead from here into the idea of mixed strategies without much difficulty.

GAME 7—Auctioning a Penny Jar (Winner’s Curse)

Show a jar of pennies; pass it around so each student can have a closer look and form an

estimate of the contents. Show students a stack of 100 pennies to give them a better idea of what

the jar might contain. While the jar is going around, explain the rules. Everyone submits a “sealed

bid”; hand out blank cards and ask students to write their names and bids on the cards and return

them. (This is also a good way for you to get to remember their names during the first meeting of

the class or the section.) The winner will pay his bid and get money (paper and silver, not

pennies) equal to that in the jar. Ties for a positive top bid split both prize and payment equally.

When you explain the rules, emphasize that the winner must pay his bid on the spot in cash.

After you have collected and sorted the cards, write the whole distribution of bids on the

board. Our experience is that if the jar contains approximately $5.00, the bids average to $3.50

(including a few zeros). Thus, the estimates are on the average conservative. But the winner

usually bids about $6.00. Hold a brief discussion with the goal of getting across the idea of the

winner’s curse.

The emphasis of this game is a concept relating to auctions that are not covered in the

text until Chapter 16. It is a simple enough game to play early in the semester if you want to

increase interest in the topics or hook additional students. One could certainly save this game

until ready to cover auctions.

GAME 8—All-Pay Auction of $10

Everyone plays. Show the students a $10 bill, and announce that it is the prize; the known

value of the prize guarantees that there is no winner’s curse. Hand out cards. Ask each student to

write her name and a bid (in whole quarters). Collect the cards. The highest positive bid wins

$10; if two or more tie with the highest positive bids, they share the $10 equally. All players pay

the instructor what they bid, win or lose.

Be sure to emphasize before bids are submitted that “This is for real money; you must

pay your bid in cash on the spot. You can make sure of not losing money by writing $0.00. But of

course if almost everyone does that, then someone can win with 25 cents and walk away with a

tidy profit of $9.75.”

Once you have collected the cards, write the distribution of bids on the board. Hold a

brief discussion about the distribution and the value of the optimal bid. This game usually leads to

gross overbidding; a profit of $50 in a class or section of 20 students is not uncommon. If that

happens, you will have to find ways of returning the profit to the class; we have done this by

having a party if the sum is large enough or by bringing cookies to the next meeting if the sum is

small. Of course, do not announce this plan in advance.

This game is also treated in Chapter 16. If you play the game on the first day, you can

lead up to at least some of the points made there, even though the analysis at this early stage

cannot go anywhere close to that level. If you prefer to follow this game with a more in-depth

discussion and, perhaps, the derivation of the formula for the optimal bid, then you want to wait

and play it when you get to Chapter 16.

Movie Excerpts

Many movies contain scenes that illustrate some aspect of strategic interaction. You can

screen these scenes in class as an introduction to that topic and let a discussion lead on to

theoretical analysis of it. Most movies or excerpts from films are best shown later in the course,

in conjunction with the particular theoretical ideas being developed. But one short scene worth

showing at the outset, because many of your students will have seen the movie, is the poison

scene from The Princess Bride. (The “poison death scene” is available in various versions on

YouTube.) In it the hero (Westley) challenges one of the villains (Vizzini) to a duel of wits.

Westley will poison one of two wine cups without Vizzini observing his action and set one in

front of each of them. Vizzini will choose a cup for himself; Westley then must drink from the

other cup. Vizzini goes through a whole sequence of arguments as to why Westley would or

would not choose one cup or the other. Finally, he believes he knows which cup is safe and drinks

from it. Westley drinks from the other. Just as Vizzini is laughing and advising Westley to “never

go against a Sicilian when death is on the line,” Vizzini drops dead.

You will want to pause the video at this point to have a brief discussion. The students will

quickly see that each of Vizzini’s arguments is inherently self-contradictory. If Westley thinks

through to the same point that leads Vizzini to believe that a particular cup will contain the

poison, then he should instead put the poison in the other cup. Any systematic action can be

thought through and defeated by the other player. Therefore, the only correct strategy is to be

unsystematic or random. This is a good way to motivate the idea of mixed strategies.

But this is not the main point of the story. Resume the video. The princess is surprised to

find that Westley had put the poison in the cup he placed closer to himself. “They were both

poisoned,” he replies, “I have been building up immunity to Iocaine for years.” Thus, the game

being played was really one of asymmetric information; Vizzini did not know Westley’s payoffs

and did not think the strategy of poisoning both cups was open to him. So you can get this idea in

at the outset of the course and tell the students that it will be discussed in greater depth in Chapter

Here is some general advice for screening movie excerpts.

DO:

1. Take suggestions from students about other movies or games you can use; their ideas

may be more appealing to other students than yours. Always ask and discuss in advance

just what strategic issue the excerpt illustrates.

2. Come prepared with a note indicating the exact time where your excerpt begins on a

DVD or with the correct YouTube URL. The effectiveness of any clip can be lost if

students have to wait for you to find it.

DON’T:

1. Don’t assume that students know the general plots of the movies from which you

show excerpts. Prepare a brief explanation of the situation and the film’s characters as it

pertains to your excerpt, and give it just before you start the DVD.

2. Don’t show a whole movie or a long clip when only a small point pertains to strategy.

The students will get distracted by the other incidental aspects.

News and Current Affairs

You will find that there is no shortage of motivation and illustration for game theory. Just

keep an eye on recent news events. These will give you several events of topical interest to tie in

with your course. More than likely, you will find examples of various concepts throughout the

semester that help you make even clearer your points about multiperson prisoners’ dilemmas,

credibility of strategic moves, the importance of patience in bargaining, and so on. Negotiations

between the government of Israel and the Palestinian authority and between the North Korean

regime and its neighboring countries and the United States provide continuing opportunities for

discussion. At a more trivial but perhaps more engaging level, so do incidents from the CBS

reality show Survivor.

One way to increase your students’ willingness or desire to apply what they are learning

to actual events is to provide a semester-long assignment requiring each of them to add to a class

collection of real-world events amenable to analysis using the theory of games. It may take them

a few weeks before they are able to do the appropriate analysis on their own, but you can add

weekly event analyses to the collection until such time as they are able to take over that role. You

do not have to restrict their examples to newsworthy events; many interesting and relevant

examples can be culled from recent films or novels. The film Waking Ned Devine, for instance,

has a wonderful example of a collective-action game and shows how individual incentives can be

different from those of the group as a whole.

Books and Web Sites

There are plenty of other sources for examples. The following books have several cases

and stories, varying greatly in their context and relevance, sometimes with an explicitly

game-theoretic analysis and sometimes without:

Steven J. Brams, The Presidential Election Game (New Haven, Conn.: Yale University Press,

1978).

Steven J. Brams, Biblical Games (Cambridge, Mass.: MIT Press, 1980).

Steven J. Brams, Superpower Games (New Haven, Conn.: Yale University Press, 1985).

Steven J. Brams and Alan D. Taylor, Fair Division (London: Cambridge University Press,

1996).

Adam Brandenburger and Barry Nalebuff, Co-opetition (New York: Doubleday, 1996).

Michael Chwe, Jane Austen: Game Theorist (Princeton, N.J.: Princeton University Press,

2013).

Avinash Dixit and Barry Nalebuff, Thinking Strategically (New York: Norton, 1991).

Avinash Dixit and Barry Nalebuff, The Art of Strategy (New York: Norton, 2008).

Paul Fisher, Rock, Paper, Scissors: Game Theory in Everyday Life (New York: Basic Books,

2008).

Erving Goffman, The Presentation of Self in Everyday Life (New York: Doubleday, 1959).

John Kay, Why Firms Succeed (London: Oxford University Press, 1995).

Paul Kennedy, ed., Grand Strategies in War and Peace (New Haven, Conn.: Yale University

Press, 1991).

John McMillan, Games, Strategies and Managers (London: Oxford University Press, 1996).

Howard Raiffa, The Art and Science of Negotiation (Cambridge, Mass.: Harvard University

Press, 1982).

Richard Thaler, The Winner’s Curse: Paradoxes and Anomalies of Economic Life (Princeton,

N.J.: Princeton University Press, 1992).

In addition, there are several Web sites dealing with game theory from the perspectives of

research, teaching, and history of thought. Here are a few URLs:

Marko Grobelnik, Robert A. Miller, and Vesna Prasnikar have some downloadable software

(for matrix games and extensive-form games) for running classroom experiments at

www.comlabgames.com/strategicplay.

For teaching and research resources and many additional links, see

David Levine, UCLA, for a focus on economic theory: levine.sscnet.ucla.edu.

Alvin Roth, Stanford University, for a focus on laboratory experiments:

web.stanford.edu/~alroth/alroth.html.

For ideas on in-class experiments, some of which are appropriate for use with topics covered in

this text, see

www.marietta.edu/~delemeeg/expernom.html

gametheory.tau.ac.il

veconlab.econ.virginia.edu/admin.htm

The latter two sites above allow your students to play games online and collect data from their

responses for your use in-class discussion. Instructor registration is required.

There is also a chronology of the subject by Paul Walker of the University of Canterbury,

New Zealand: www.econ.canterbury.ac.nz/personal_pages/paul_walker/gt/hist.htm.