entire book even if you skip all these questions, struggling with them will make you a
stronger player.
This book will challenge your intellect by showing how strange and seemingly
paradoxical results manifest themselves when humans compete. Among this book's
lessons are the following:
Never hire someone too eager to work for you.
Have less trust in smokers.
Many people in business exhibit honesty not because they are moral but
because they are greedy.
Eliminating choices can increase your payoff.
Burning money can increase your wealth.
Stock prices respond quickly to new information.
Day-traders still need to worry about their stock's long-term prospects.
Exposing yourself to potential humiliation can increase your negotiating
strength when seeking a raise.
Inmates in mental institutions have a few negotiating advantages over their
somewhat more sane corporate counterparts.
Learning about Odysseus' recruitment into the Trojan War provides insight
into why stores issue coupons.
You might ask, 'Will reading this book help me make money?' A true game-theoretic
answer might be that since you have probably already bought this book, I don't really
care what benefit you would receive from reading it, so why should I bother answering
the question? In fact, you likely only purchased this book after reading the jacket, the
table of contents and maybe the first paragraph of the introduction. Perhaps I should only
bother putting a lot of effort into these very small parts of the book and just ramble on for
the rest of it to fill up space. For the rest of the book I could just ramble on and on by
being very, very, very verbose as I repeat myself over and over again by just rambling on
to fill up the space that I have to fill up for you to think that this book is thick enough to be
worth the book's purchase price. After all, I have more important things to do in my life
than write for the pleasure of people I have never even met. Of course, I like money, and
the more copies of this book that sell, the more money I'll get. If you do like this book,
you might suggest to a friend that she buy a copy. Also, if I choose to write another book,
you will be more likely to buy it if you enjoy this one, so probably for purely selfish
reasons I should make some attempt to provide you with useful information. Furthermore,
as of this writing my publisher, McGraw-Hill, still has the contractual right to reject this
manuscript. Since McGraw-Hill is a long-term player in the publishing game, they would
be harmed by fooling book buyers into purchasing nicely wrapped crap. Alas, this means
that if I manifestly fail to put anything of value in this book my publisher will demand the
return of my advance. Beware, however, if you end up enjoying this book, it's not
because I wrote it for the purpose of making you happy. I wrote it to maximize my own
payoff. I don't care, in any way, about your welfare. It's just that the capitalist system
under which books are produced in the United States creates incentives for me to
seriously attempt to write a book that customers will enjoy and perhaps even benefit from
reading.
[1]
Browning (1989), 384.
What Exactly Is Game Theory?
There are three parts to any game:
A set of players
Moves the players can make
Payoffs the players might receive
The players choose their moves to maximize their payoff. Each player always assumes
that other players are also trying to maximize their score.
Game theory gets interesting, however, only when there is tactical interaction, that is,
when everyone tries to figure out their rivals' strategy before they move. Football
(American or European) could be analyzed using game theory because the players try to
determine their opponents' strategy before making their move. Bowling and golf are not
interesting to game theorists because although players compete in these sports, they
mostly ignore their competitors when formulating their moves because they have no
control over how their competitor might play.
Mathematics dominates much of formal game theory. In an attempt to maximize this
author's book royalties, however, Game Theory at Work keeps the math to a minimum.
Fortunately, you can learn most of the practical applications of game theory without
using any math more complicated than addition and subtraction. This book does,
however, contain many figures and diagrams, and if you skip them you will learn little.
In game theory land people always act in their own self-interest, and consequently
everyone lies whenever lying serves their interests. So, how can you make your threat or
promise believable when your word is worthless? Chapter 2 considers the credibility of
threats and promises.
Chapter 2: Threats, Promises, and Sequential
Games
Overview
“A prince never lacks legitimate reasons to break his promise.”
Machiavelli
[1]
One summer while in college I had a job teaching simple computer programming to
fourth graders. As an inexperienced teacher I made the mistake of acting like the
children’s friend, not their instructor. I told the students to call me Jim rather than Mr.
Miller. Alas, my informality caused the students to have absolutely no fear of me. I found
it difficult to maintain order and discipline in class until I determined how to threaten my
students.
The children’s parents were all going to attend the last day of class. Whereas the
students might not have considered me a real teacher, they knew that their parents
would. I discovered that although my students had no direct fear of me, they were afraid
of what I might tell their parents, and I used this fear to control the children. If I merely
told two students to stop hitting each other, they ignored me. If, however, I told the
children that I would describe their behavior to their parents, then the hitting would
immediately cease.
The children should not have believed my threat, however. After the summer ended, I
would never see my students again, so I had absolutely nothing to gain by telling the
parents that their children were not perfect angels. It was definitely not in my interest to
say anything bad about my students since
It would have upset their parents.
I realized that their bad behavior was mostly my fault because I had not been
acting like a real teacher.
The people running this for-profit program would have been furious with me
for angering their customers.
Since they were only fourth graders, it was understandable that my students (who were
all very smart) didn’t grasp that my threat was noncredible. When making threats in the
business world, however, don’t assume that your fellow game players have the trusting
nature of fourth graders.
Let’s model the game I played with my students. Figure 1 presents a game tree. The
game starts at decision node A. At node A, a child decides whether or not to behave,
and if he behaves, the game ends. If he doesn’t behave, then the game moves to
decision node B; and at B I have to decide whether to tell the parents that their child has
misbehaved. In the actual game the children all believed that at B I would tell their
parents. As a consequence the children chose to behave at A. Since it was not in my
interest to inform the parents of any misbehavior, however, my only logical response at B
would be to not tell their parents. If the children had a better understanding of game
theory they would have anticipated my move at B and thus misbehaved at A. My
students’ irrational trust caused them to believe my noncredible threat.
Figure 1
[1]
The Prince (1514), Chap. 18.
Controlling a Wild Daughter
Parents, as well as teachers, often try to control their children’s behavior with threats.
Imagine that two parents fear their wild teenage daughter will become pregnant. First,
they try reason and urge her to be more careful. But when reason fails, the parents
resort to threatening to disown their daughter and kick her out of the house if she
becomes pregnant. Should the daughter believe her parents’ threat? Not if she knows
that her parents love her.
If the daughter trusts in her parents’ love, then she will believe that the threat was made
to improve her welfare. If the daughter became pregnant, she would need her parents
more than ever. The daughter should thus realize that her caring parents would devote
even more resources to her if she got pregnant. An intelligent but still wild daughter
should ignore her parents’ threat as lacking credibility. Sure, loving parents might
threaten their daughter to dissuade her from having sex. If she gets pregnant, however, it
would not be in the interest of caring parents to actually carry out the threat. The
manifest love of the parents weakens their negotiating strength. Interestingly, if the
daughter suspected that her parents didn’t love her, then she might believe their threat,
and all three of them would be better off.
Circumstances in life and business often arise where you would gain from making a
believable threat. Unfortunately, game theory shows that many threats can and should
be ignored, since a man is never as good as his word in game theory land. Game theory,
fortunately, provides many means of making credible threats.
Eliminating Options
Normally, you benefit from choices. We usually think that the more options we have, the
more ways we might profit. The existence of some choices, however, increases the
difficulty of issuing credible threats. Consequently, eliminating options can increase your
payoff.
Imagine that you're a medieval military commander seeking to capture the castle
depicted in Figure 2. Your troops have just sailed over on boats to the castle's island.
Everybody knows that if you were determined to fight to the end, then your army would
ultimately be victorious. Unfortunately, the battle would be long and bloody. You would
lose much of your army in a full-blown battle for the castle, so you desperately pray for
your enemy's surrender. Since the enemy knows that it would lose the battle, one might
think that it indeed should surrender.
Figure 2
Unfortunately, your enemy has heard of your compassion. You don't care at all about the
welfare of the enemy, but you do worry about the lives of your own soldiers (perhaps for
selfish reasons). The enemy correctly suspects that if it holds out long enough, you will
be sickened by your losses and retreat, for although you desire the castle, you wouldn't
decimate your army to obtain it.
Your opponents would immediately capitulate if they believed you would fight to the end,
so if you could make a believable threat to fight until victory, they would give up and you
would not have to risk your troops. Unfortunately, a mere threat to fight to the finish lacks
credibility, so what should you do? You should burn your own boats!
Imagine that if your boats were burned, it would take many months for your allies to bring
new boats to the island to rescue your army. Meanwhile, you would perish if you did not
occupy the castle. Losing your boats would compel you to fight on until victory. More
important, your enemy would believe that with your boats burned you would never retreat.
Surrender is the optimal response of the enemy to the burning of your boats. By
destroying your boats, you limit your choices. You can no longer take the easy way out
of the battle by retreating. Eliminating the option of retreating makes your threat credible
and allows you to win a bloodless victory.
Cortez, conqueror of the Aztecs, employed this boat-burning tactic.
[2]
Shortly after
landing in Mexico, Cortez destroyed his ships, thus showing his potential enemies and
allies that he would not be quickly driven back to Europe. Consider the effect this tactic
had on local tribes that were considering allying with Cortez against the powerful Aztecs.
No tribe would want to ally with Cortez if it thought that he might someday abandon his
fight against the Aztecs and return to Europe, for then the tribe would be left to the mercy
of their mighty human-sacrificing neighbors. Cortez would likely have promised local
tribes that regardless of how poorly he did in his fight against the Aztecs he would not
leave until they were vanquished. Such a promise, by itself, was not believable. If Cortez
had not burned his ships, his potential allies would have thought that Cortez would run
away if he suffered an early defeat. By burning his ships and eliminating the option of
quickly retreating to Europe, Cortez guaranteed that he wouldn't leave his allies. As we
shall see, eliminating options can be a useful strategy in business as well as military
negotiations.
[2]
Dixit and Nalebuff (1991), 152-153.
Asking for a Raise
You desperately desire a $20,000 per year raise. The company you work for likes money
as much as you do, however, so you will get the raise only if you can convince your boss
that it is in her interest to give it to you. But why should your boss give you a raise? Why
is it in her interest to be “nice” to you? If you have any chance at getting a raise, you
contribute to your company, which would be worse off without your labors. Your best
chance of obtaining a raise, therefore, lies in convincing your boss that you will leave if
you don’t get the money.
If you simply tell your boss that you will quit if you don’t get the raise, she might not
believe your threat. For your boss to take your threat to quit seriously, she must think
that it would be in your self-interest to walk away if you’re not given the money. The best
way to make your threat credible would be to prove to the boss that another company
would pay you $20,000 a year more. (Of course, if you’ve found another firm that’s
willing to give you the raise, then you don’t need to read a book on game theory to learn
how to get the extra $20,000.)
Another way to get the raise would be to tell everyone in the firm that you will definitely
quit if you don’t obtain it. Ideally, you should put yourself in a position where you would
suffer complete humiliation if you were denied the money and still stayed in your job.
Your goal should be to make it as painful as possible for you to stay if you weren’t given
the salary increase. This tactic is the equivalent of reducing your options. By effectively
eliminating your choice to stay, your boss will find it in her self-interest to give you the
money because she knows you will have to leave if you don’t get the raise.
Figure 3 presents the game tree for this raise negotiation game. The game starts at A
where you ask for a raise. Then at B your boss has the option of giving it to you or not. If
she does not give you the raise, the game moves to C, where you either stay at your job
or quit. There are thus three possible outcomes to the game, and Figure 3 shows what
your boss gets at each outcome. Obviously, your boss would consider giving you the
raise only if she knew that at C you would quit. So, you need to make your threat to quit
credible. You do this either by getting a high payoff if you quit or a low payoff if you stay,
given that your raise request was rejected. Interestingly, if you got your raise, then the
game would never get to C. Your boss’s perception of what you would have done at C,
however, was still the cause of your triumph. Often, what might have happened, but
never did, determines the outcome of the game.
Figure 3
Relinquishing Control
Giving up control of events can also strengthen your negotiating position. Imagine that
you’re now a manager trying to resist wage increases. Your employees are extremely
valuable to you, but unfortunately your workers are aware of their importance and know
that you would be reluctant to lose them. You consequently have a weak negotiating
position, for if your employees could ever convince you that they would leave if not given
a raise, then you would give in to their salary demands. Giving up control of salary
decisions could free you from this dilemma. Relinquishing control allows you to credibly
claim that you can’t increase wages.
Of course, your precious employees could play their games with the people who now
make the salary decisions. But these new salary setters might not care if an employee
left. For example, the loss of an efficient secretary who understands your routine would
be devastating. If the secretary grasps his importance, he has a very strong negotiating
position if you have the power to grant him a raise. A manager in human resources,
however, might not care if your efficient secretary quit. If your secretary had to negotiate
with this indifferent manager, then his position would be weakened because the HR
manager would be more willing to allow your secretary to leave the company than you
would.
Telling others that you have given up control is a common negotiating tactic. When
lawyers try to settle lawsuits, they often claim that their client has authorized them to go
only to a certain amount. If this limitation on the lawyer’s authority is believed, then the
lawyer’s promise to never accept a higher offer is credible. Broadcasting your lack of
decision-making authority makes it easier to turn down unwanted requests.
An ancient English law punished communities that paid tribute to pirates.
[3]
Had a coastal
community merely told pirates that they would never pay tribute, the pirates would
probably not have believed them. The ancient law, however, made their statement more
credible by effectively eliminating the option of paying tribute.
Smith College, where I teach, has a similar antitribute law that protects professors from
students. At Smith College professors are not permitted to grant students extensions
beyond the last day of finals, so students must go to their deans for such extensions.
One might think this policy signals that Smith professors are administratively weak
relative to deans. In fact, professors dislike dealing with students asking for extensions,
so Smith professors are consequently made better off by a rule that circumscribes their
extension-granting abilities. Managers can similarly benefit from limitations on their
authority. Many managers, like professors, desire popularity and consequently dislike
having to turn down their peoples’ requests. It’s much easier to say no when everyone
understands that you lack the ability to say yes.
[3]
Schelling (1960), 19.
Cutting Off Communications
Giving up control by cutting off communications would also help you capture our
hypothetical castle. Recall that in the battle for the castle your enemies will surrender
only if they believe you will fight until victory. To credibly commit to never retreating, you
could first order your troops to fight to the death, then leave your troops behind on the
island. If your enemies see you leave and believe that no one else on the island has the
ability to call off the attack, then they will think that your troops will fight to the end.
Cutting off communications can be useful in business negotiations as well. For example,
imagine facing a buyer who won’t accept your current offer because she believes you will
soon make a better one. To credibly convince this buyer that you won’t lower your price,
you could make one final offer, walk away from the negotiations, and then not return the
buyer’s calls, faxes, or e-mails. Refusing contact can enhance credibility.
In a 1965 prison riot a warden refused to listen to prisoner demands until they released
the guard hostages.
[4]
By refusing to even listen to the prisoners, the warden made
credible his implicit promise never to give in.
[5]
Likewise, if an employee constantly
pesters you for a salary increase, refusing to even listen to her demands credibly signals
that she has no chance of prevailing.
[4]
Davis (1970), 107–108.
[5]
Ibid.
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