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CHAPTER 9
Strategic Moves
Teaching Suggestions
The ideas in this chapter can be brought to life and the students can better appreciate the
subtleties of various strategic moves and their credibility if you hold classroom discussions based on
situations where such strategies are of the essence. Depending on your preference, you can either have the
discussion before any formal analysis is done and use the ideas that arise in your discussion to develop the
analytical concepts and techniques, or you can do things the other way around. Similarly, because
brinkmanship is critically linked to the issues covered in this chapter, you may find that you want to cover
Chapter 14 before attempting the discussions described below, or you may want to use these discussions
as a springboard for the analysis provided there.
We have found that students have the most difficulty grasping the distinction between deterrence
and compellence. It is often especially hard for them to identify the four possible types of threats and
promises and the circumstances in which the various combinations can best be used. You may want to
take the time to construct specific examples of each type of threat and of scenarios in which each is most
likely to be used. We emphasize two points: (1) deterrent threats and compellent promises are the most
common conditional response rules, and (2) compellent threats and deterrent promises require that the
player making the strategic move impose some type of time limit on the rival. In discussion with the class,
students usually connect the fact that point 2 helps explain why point 1 holds.
To convey the basic ideas of commitments, threats, and promises using examples other than those
in the book, you can try some of the examples from Dixit and Nalebuff, Thinking Strategically, Chapter 5.
We also provide some additional examples here.
For a commitment example, you can return to the battle of the sexes example described in the
teaching suggestions for Chapter 4; the game was between a husband and wife trying to decide on a film
to see, Independence Day or The English Patient. This game has two Nash equilibria in pure strategies
(and one in mixed strategies). Either player in this game could use a strategic move to better his or her
expected equilibrium payoff. By restricting her own freedom of action, for instance, the wife could
commit to seeing The English Patient; she could do so by spending her last $8 on a ticket for that film. Or
the wife could take some action that changed the payoffs in the game, changing her payoff from seeing
Independence Day with her husband to –1 instead of 1; perhaps his behavior during such films makes it
even worse for her to see them with him rather than without him. In either case, the unique Nash
equilibrium of the game becomes (The English Patient, The English Patient).
You can then cover the standard practical difficulties that one must consider with commitment
moves. The other player (the husband here) may not receive the necessary information about your
commitment move; this may be a deliberate move on the other player’s part. In addition, the other player
may not believe your commitment; this brings up issues of credibility. Finally, simultaneously clashing
commitments may lead to a bad outcome.
For a different example of a game in which a threat can alter the outcome to a player’s benefit,
consider a sequential game between you and a mugger: you make the first move and decide whether to
give up your wallet; then the mugger decides whether to stab you. The tree for this game in its original
(no strategic move) format is illustrated below:
Rollback shows that never stab is a dominant strategy for the mugger in the absence of any strategic
moves; given this, you choose not to give up your wallet. The subgame-perfect Nash equilibrium is (not,
never stab), and payoffs in equilibrium to you and the mugger are (4, 2). You get your highest possible
payoff and can do nothing to improve your payoff in this game, but the mugger can make a threat to
change the path of play and improve his outcome.
The mugger can use a threat: “If you don’t give me your wallet, then I will stab you.” This is a
compellent threat with an implicit promise that you will not be stabbed if you do hand over your wallet. If
you believe the threat, then it is in your interest to give wallet (and get a payoff of 3) rather than not (and
get a payoff of 2). Of course, it is not optimal for the mugger to carry out the threat if put to the test
(mugger gets 1 instead of 2 if he follows through due to the risk of a felony conviction and a long prison
term), so credibility is problematic. The mugger could establish credibility in this case through
irrationality—acting crazy and out of control.
For an example of a promise, you can use a variant on the parent-child game from Exercise U2 in
this chapter. The tree for a sequential version of that game (with slightly different payoffs than those
described in the exercise) is shown below:
Payoffs assume that the Child prefers outcomes with a Big gift over those without a gift and then prefers
to Party rather than Study; the parent wants the child to Study above all and then prefers outcomes in
which no gift is necessary. The Nash equilibrium shows that the parent chooses No regardless of the
child’s choice, so the child chooses Party rather than Study. The payoffs are 2 to the child and 2 to the
parent.
The parent can improve his outcome—and get the child to Study—by using a compellent
promise: “If you study, I will give you a big gift.” The implicit threat here is that there is no big gift if the
child parties; this is automatically credible given the payoff structure of the game. The credibility of the
promise is questionable because purchasing the big gift is not in the parent’s best interest once the child
has done the studying. The parent can establish credibility of such a promise with a reputation for
following through; this works especially well for children with older siblings.
Finally, for an example of a game that requires both a threat and a promise, consider this example
about the U.S. House of Representatives vote on Reagan’s 1981 tax cut bill. (This example comes from
Dixit and Nalebuff, Thinking Strategically, pp. 131–135 and is based on a New York Times article by
Leonard Silk from April 10, 1981. Its formal structure is similar to that of the U.S.-China joint action
game in Section 4.C of this chapter.) The payoff table for the game between the Democrats and
Republicans in the House is as follows:
Republicans
Hard-line support Compromise
Democrat
s
Weak opposition 2, 4 3, 3
Hard-line attack 1, 2 4, 1
The payoff structure depends on the following considerations related to the various outcomes. In the
(Weak opposition, Hard-line support) cell, there is a Republican victory and the Democrats maintain the
ability to say, “Don’t blame us.” In the (Weak opposition, Compromise) cell, the Republicans win but not
totally; Reagan is unhappy and the Democrats get to share the credit. In the (Hard-line attack, Hard-line
support) cell, Reagan’s program is blocked in the House and the Democrats get the blame for thwarting a
popular president. Finally, in the (Hard-line attack, Compromise) cell, the Republicans lose much of their
program and the Democrats look fiscally responsible.
The Nash equilibrium of the game without strategic moves entails Weak opposition by the
Democrats and Hard-line support by the Republicans; payoffs are (2, 4). The Democrats have an incentive
to use a strategic move to better their outcome. They could try to use a commitment move, but
committing to Hard-line attack leaves them with a payoff of 1 instead of the 2 they get with Weak
opposition, so a commitment does not help. Instead, they must consider a threat and/or a promise.
For a threat, the Democrats would want to say, “If you give Hard-line support, we will offer
Hard-line attack.” This is not immediately credible since Hard-line attack is not in the Democrats’ best
interest if the Republicans offer Hard-line support. Similarly, the implicit promise that goes along with
this threat—“If you compromise, so will we”—is not credible since Weak opposition is not the choice the
Democrats would want to make against compromising Republicans. (If the Democrats wanted to make
just the promise, they would find that its implicit threat was not credible.) The Democrats must use a
combination of a threat and a promise, explicitly stating both parts of the response rule: “We will match
compromise for compromise, hard line for hard line.” Both parts need to be made credible as well,
potentially through the establishment of a reputation in the ongoing (repeated) game between House
Republicans and Democrats. In reality, this did not happen.
You may find it useful to come up with your own, perhaps university-specific, examples of
methods by which players can enhance the credibility of their strategic moves. For universities with an
honor code, the credibility of such a code can provide an excellent discussion topic for this chapter. Also,
the text discusses how “apparently irrational motives like honor or face” may make it credible that you
will deliver on a promise. One possible example of this is the tradition of the U.S. Marines never to leave
any of their dead behind on the battlefield; inculcating this philosophy into all Marines may make credible
a great deal of trust between soldiers.
As for the discussion topics we mentioned earlier, there are four different scenarios that we have
used in order to stimulate class discussions. The first concerns governments’ negotiations with terrorists
who are holding hostages. We consider the typical situations in which such negotiations arise, the types of
policies governments consider, and the credibility issues that arise, as well as the various components of
the negotiations themselves.
A second possible topic is the game between political prisoners and their jailers. The inspiration
for this discussion came from reading Nelson Mandela’s Long Walk to Freedom (Boston: Little, Brown,
1994), especially the chapters “Robben Island: The Dark Years” and “Robben Island: Beginning to
Hope.” This topic proved a good way to get across the point that even though your sympathy is entirely
on one side, to understand and analyze the game properly, you must also understand the strategies and the
objectives of the other side.
The third topic that we use for discussion is the film Dr. Strangelove. We schedule an extended
session of the class and screen the movie, which lasts 95 minutes, or have the students watch it online
(“video reserve”) for homework. In the following class session we hold a discussion on the strategic
issues that arise in the movie. This movie is full of incidents where threats, promises, credibility, and so
on are of the essence. In movie-buff polls it is often ranked in the all-time top-10 lists, and it engages the
interest of most of our students. But it is in black and white, it lacks modern visual special effects, and its
premise of superpower nuclear confrontation is ancient history to many of today’s students. If you want to
use this film and have the technology available, you can use clips from YouTube during the discussion
class to show critical scenes as they are brought up for discussion. You can instead use Dr. Strangelove in
conjunction with Chapter 14; the impact is perhaps greater if the class sees it while the drama of the
Cuban missile crisis is fresh in their minds.
Finally, a fourth option is to use a number of brief individual scenes where strategic moves are
played from several more recent movies. You might be able to arouse greater interest in such films than is
possible with Dr. Strangelove. Further, if you can put together a set of clips, from YouTube, for example,
that assembles such scenes from a number of movies, you can get more varied and more modern settings
and use these as the basis for your discussion. We have recently tried this approach, providing links to
clips for students to view and comment on electronically. This procedure allows for an ongoing
conversation that continues beyond the bounds of a 50- or 70-minute class period; as an added bonus, you
get a record of the conversation using this method.
For your guidance, we append summaries of our discussions of each of these topics. We do this
with a twofold purpose. If you choose one of these topics, these summaries will give you points with
which you can lead the discussion in interesting directions if it begins to lag or go off in irrelevant
directions. If you choose some other topic, these summaries may suggest general ideas about organizing
your own topic ahead of time and being ready to offer pointers to the class. We apologize for the terse and
note-like (often ungrammatical) quality of these summaries; a fuller version would be too long.
DISCUSSION TOPIC 1: STRATEGIES AGAINST HOSTAGE TAKERS
Typical Situations
Terrorists: usually have several hostages, demands are political, may be fanatics, location may be
public or secret, local or foreign
Prison riots: guards as hostages, demands for improved conditions
Kidnapping for ransom: usually a single hostage, demands monetary, usually calculatingly rational,
location secret
Policy to Deter Hostage Taking
When asked what policy the government should announce in advance, there is general agreement
that the government should declare that it would never negotiate. This gets at the idea of a commitment.
But when an actual incident is depicted, with the hostages’ relatives’ appearing on TV news asking what
the government is going to do, most students recognize that the government would abandon its policy and
negotiate. This at once brings home the idea of credibility or lack thereof. (For a film version of such a
situation, you can use the example of Harrison Ford as president in Air Force One.) But one or two
students in the class generally argue for being tough even though this means the loss of some lives. Dis-
cuss this for a while, and bring out the idea that in different countries and at different times, political and
social norms differ, and hanging tough may be feasible in some cases but not others. The current U.S.
setting makes it particularly difficult for the authorities to act tough.
The terrorists may take advantage of the pressure that media and relatives can create by taking
hostages most likely to arouse sympathy—the old, the sick, or children.
Some suggestions to enhance the credibility of a tough stance or the reputation of a government
trying to take such a stance:
1. Stage a fake incident and resolve it with the terrorists giving in. This may do more harm than good if
the truth leaks out.
2. Give the power to retaliate into the hands of an independent bureau or organization like the army.
(This leans toward brinkmanship, which is covered in Chapter 14.) But in the United States there are
always civilian overrides.
3. Make laws that punish anyone who communicates or deals with terrorists. But again someone or
some group can override such laws in a good cause. Thus there is no really good solution in open
democratic societies; totalitarian ones have an advantage in this regard.
There is a distinction between terrorism and kidnapping: with the latter, the victim’s relatives can
capitulate against the government’s wishes. The government can try to prevent them from doing so, for
example, by freezing their assets. But then in future incidents the relatives may settle secretly without
ever notifying the authorities. (It was pointed out that kidnappers would make a mistake by choosing a
victim who has sole control over the assets from which the ransom is to be paid; better for them to take
the dependent spouse or child of such a person.)
Even if it seems likely that the government will negotiate when an actual incident occurs, there is
some uncertainty, and the policy announcement may serve to deter some of the milder or less fanatical
potential terrorists.
Negotiations
Several issues arise and each situation has its special features. In one sense the terrorists or
kidnappers start out with an advantage; they choose the time and location and are better organized. But
governments also prepare and train teams to handle such situations. Some terrorist groups also have a
reputation for toughness or fanaticism, while some governments have the opposite reputation.
