The economics of high-visibility terrorism

www.elsevier.com/locate/econbase

European Journal of Political Economy

Vol. 20 (2004) 479–494

The economics of high-visibility terrorism

Sanjay Jaina,*, Sharun W. Mukandb

aDepartment of Economics, University of Virginia, 114 Rouss Hall, Charlottesville, VA 22903, USAbDepartment of Economics, Tufts University, Medford, MA 02144, USA

Available online 17 April 2004

Abstract

This paper analyzes some implications of very visible, discrete, large-scale terrorist actions, such

as the September 11 attacks. By becoming part of the set of common knowledge, such events of mass

terror have direct implications on both the supply and composition of the ‘mix’ of terrorist attacks, as

well as responses to them. First, we analyze the implications of greater anti-terror operations on the

quantity as well as the mix of terrorists supplied by terrorist organizations. Second, we present a

novel argument for the role of public announcements in endogenously coordinating responses in the

face of a terrorist-hijacking. Public announcements, by injecting strategic uncertainty, can give rise to

a Pareto-superior outcome, at minimal resource cost to the government.

D 2004 Elsevier B.V. All rights reserved.

JEL classification: D74; D82; C72

Keywords: Mass terror; Visibility; Common knowledge; Coordination; Negotiation

1. Introduction

One of the most distinct aspects of the event of mass terror witnessed on September 11th,

was its ‘visibility’. The high visibility had an immediate and dramatic effect on the

information sets and beliefs of all agents—potential victims, government, law enforcement

agents, as well as terrorists. Although suicide attackers had previously inflicted casualties in

the Middle East, and had attacked US targets in Lebanon and Yemen, the high visibility of

the September 11 attacks meant that, at one stroke, the presence of suicide terrorists became

‘common knowledge’ amongst all agents. This paper analyzes the implications of such a

visible event of mass terror on the incentives of terrorists, law enforcement as well as the

potential victims. We use game-theoretic analysis to examine two related questions. First,

0176-2680/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.ejpoleco.2004.02.001

* Corresponding author. Tel.: +1-434-924-6753; fax: +1-434-982-2904.

E-mail address: [email protected] (S. Jain).

S. Jain, S.W. Mukand / European Journal of Political Economy Vol. 20 (2004) 479–494480

what is the likely impact of such an event of mass terror on the mix of terrorists supplied by

terrorist organizations? Second, we consider the impacts of such acts of mass terror on the

likely responses of law enforcement, the government and potential victims, and use that to

derive the implications of a particular policy proposal.

A starting point of our analysis is that we do not see terrorists who are willing to commit

suicide as irrational zealots, but rather as instruments used by terrorist organizations to

achieve their goals.1 Once we treat acts of terrorism as being conducted by rational actors,

anti-terror policies such as increased vigilance, and the devotion of greater resources to law

enforcement and anti-terror operations, can have consequences that are not obvious. It is

well understood from the literature on the economics of crime and punishment that greater

resources allocated to anti-terror operations will have a negative impact on the level of

terrorism (see Becker, 1968, and the survey by Sandler and Enders, 2004). However, we

show that although increased anti-terror operations decrease the level of terrorism, themix or

composition of terrorists may shift adversely, towards those who are more willing to use

more extrememethods. Indeed this shift in the mix of terrorists arises not because of any new

information about their effectiveness, but rather precisely because of the increased vigilance

of law enforcement as well as potential victims (such as airline passengers). This shift in the

composition of terrorists takes place for purely strategic reasons and is quite different from

the reasons identified in the literature on the roots of terrorism (see, for example, Krueger and

Maleckova, 2002). Our analysis is closer in spirit to Sandler et al. (1983) and Landes (1978),

who focus on how an increase in penalties and law enforcement affects terrorists’ incentives.

In contrast to their analysis, however, the focus of our analysis is not the tradeoff between

terrorism and other activities, but rather on the tradeoff between alternative ‘means’ of

terrorism to achieve the same end.

The dramatic visibility of the mass terror of September 11th and the willingness of the

terrorists to commit suicide has had a second important effect—on the incentives of potential

victims to choose between alternative actions. In particular, the fact that the dramatic

demonstration of the possibility of suicide terrorists is common knowledge gives rise to a

multiplicity of equilibria. Depending on their beliefs about the possibility of coordinating

resistance with their fellow passengers, a passenger may prefer to cooperate with or resist

against the terrorists. As is well understood, this multiplicity of equilibria associated with

self-fulfilling beliefs is a consequence of the ‘common knowledge’ of fundamentals by all

agents. However, less well understood is the fact that the government can take advantage of

this situation by introducing strategic uncertainty through public announcements—which

remarkably, will result in a unique equilibrium, where passengers resist the terrorists. For

instance, the public announcement of the introduction of sky marshals in flights can serve as

a coordinating device, such that passengers end up endogenously attacking terrorists, even

though they are aware that there are no sky marshals on the flights. This remarkable insight

1 This point has been forcefully made by Sprinzak (2000), who argues that ‘‘suicide terrorism has inherent

tactical advantages over ‘conventional’ terrorism: It is a simple and low-cost operation (requiring no escape routes

or complicated rescue operations); it guarantees mass casualties and extensive damage (since the suicide bomber

can choose the exact time, location, and circumstances of the attack); there is no fear that interrogated terrorists

will surrender important information (because their deaths are certain); and it has an immense impact on the

public and the media (due to the overwhelming sense of helplessness).’’

S. Jain, S.W. Mukand / European Journal of Political Economy Vol. 20 (2004) 479–494 481

draws on recent work by Morris and Shin (1998, 1997) on the role of ‘almost common

knowledge’ in generating unique equilibria in coordination games.

It is useful to distinguish this result from themore standard result common to the literature

on random audits or costly state verification (Townsend, 1979) or the literature on the

economics of crime. Our claim is not that introducing costly sky marshals (or any other anti-

terror investments) in flights, by lowering the ability of terrorists to carry out a successful

hijacking, will reduce the incidence of plane hijacking. That we take to be self evident.

Rather, our insight is more subtle and relies on the fact that when common knowledge about

the presence (or absence) of sky marshals no longer holds, then that is enough to induce a

unique equilibrium where passengers endogenously choose to resist hijackers in a coordi-

nated fashion. The role played by information in our analysis is quite nuanced. Even if all

passengers are aware that there are no skymarshals on the flight, so long as they are unsure of

the beliefs of the other passengers, a unique equilibrium, in which passengers resist, may

arise endogenously. More generally, our analysis highlights the importance of public

announcements by the government, and suggests that even terrorist warnings can (under

some conditions) be much more effective than is commonly thought.

There is remarkably little related literature in this area, on the application of game-

theoretic tools to model decision-making in the context of hijackings and hostage-taking.2

This is surprising given the importance of formulating policy responses to counteract and

respond to terrorism, even before the September 11 attacks, and the applicability of

available tools in the theoretical literature on game theory and models of asymmetric

information. For example, Sandler and Enders (2004) identify a mere handful of papers

that deal with the economic analysis of hostage-taking events, of which only three utilize

game-theoretic tools in any depth—Atkinson et al. (1987), Selten (1988) and Lapan and

Sandler (1988). We differ from these analyses in that we focus on the composition of

terrorists, and not just the level of terrorism. Indeed a distinctive feature of our analysis is

that we explore the incentives of terrorist organizations from alternative strategies—e.g.,

suicide-hijackers as against the more conventional hijackers who are willing to negotiate.

By examining both the supply of terrorists as well as the endogenous response of potential

victims of terror, we identify a potential multiplicity of equilibria, and suggest insights into

how the equilibrium might change.

The importance of governments coordinating their responses to terrorist actions is

emphasized in other lines of research. For example, in choosing the levels of deterrence

effort (or expenditure) to undertake, governments impose a ‘transference externality’ on one

another when deterrence levels are chosen independently. This externality can be positive or

negative, depending on the relative strength of two opposing effects: on the one hand,

country A’s deterrence efforts make country B’s citizens safer (by making attacks on them

less likely in country A). On the other hand, increased deterrence in country A also shifts the

attacks abroad, to country B. The analysis of remedies again emphasizes the importance of

increasing coordination among countries, and points out that a piecemeal approach is likely

to be unsuccessful. Similarly, in choosing retaliatory action against the terrorists, co-

ordination may be key. Typically, the cost of retaliation (in terms of attracting subsequent

terrorist actions) is privately borne, whereas the benefit accrues to all countries. In this

2 For a survey, see Sandler and Enders (2004).


situation, the classic prisoners’ dilemma prediction is that governments under-provide a

resource that has value to all (Lee, 1988; Sandler and Enders, 2004). Again, as with most

public good provision problems, a coordinated response can go some way to solving this

problem. This is further explored in Kunreuther and Heal (2002), who examine the role of

tipping mechanisms in ensuring coordinated investments and responses to terrorism.

Our analysis of the coordination problem differs from these analyses in that we focus

on implicit rather than explicit coordination. In other words, there is no overt coordination

among the concerned parties, for example, among passengers and flight crew choosing

whether to attack aircraft hijackers. Such communication may simply be impossible in the

circumstances. Thus, convergence to a (new) equilibrium happens because public

announcements by governments, by injecting strategic uncertainty amongst the affected

parties, may affect beliefs sufficiently to ensure endogenous coordination at a unique

equilibrium. Strikingly, this coordination is predicted to occur in the absence of any formal

coordinating agency.

The paper is organized as follows. Section 2 examines how the choice among

alternative means of terrorism is influenced by terrorists’ expectations of the level of

resistance that they might encounter, for example, from potential victims. In Section 3, we

examine the role of public announcements in generating strategic uncertainty and enabling

endogenous coordination amongst potential victims. Section 4 concludes.

2. Resistance and the supply of terrorists

We begin by looking at the ‘supply’ of terrorists—or, more accurately, at the composition

of the mix of various means used by terrorists in the pursuit of their political or ideological

aims. We model the ‘choice of technique’ by (potential) terrorists as the outcome of an

optimization decision by the terrorists (or terrorist groups), given the underlying parameters

regarding the level of resistance and deterrence they are likely to encounter, their own

willingness to kill or be killed, etc. In this section, we relate this choice decision, and the

resultant composition of terrorist actions, to the anticipated level of resistance from the

potential victims and deterrence by government agencies. In the next section, we conduct the

complementary analysis: for a given mix of terrorist actions, we describe the potential

victims’ responses, and use the resultant equilibria to analyze the implications for a particular

policy proposal, viz., the introduction of sky marshals on some airline flights.

We model heterogeneity among (potential) terrorists as resulting from variations in their

‘type’, denoted by h, which we can interpret as the propensity towards violence, or the

willingness to shed blood in pursuit of their objectives. If the terrorist decides on violent

means to pursue his or her cause, then we consider two possible ways in which outcomes

can be achieved.3 One is to carry out an attack with the objective of extracting concessions

from the government—e.g., to seize hostages by hijacking an aircraft, with the objective of

negotiating for a ransom, or the release of previously captured colleagues. We denote this

course of action by N (the mnemonic for Negotiation, which is the ultimate aim of carrying

3 More generally, the terrorist (group) can choose from a range of possible actions. For simplicity, the model

focuses on only two strategies.


out the action). The other course of action that the terrorist can adopt is to launch a suicide

attack (denoted by S), with the objective of causing large-scale death and destruction.4 By

focusing on these two choices, we are implicitly assuming that, for terrorists, these actions

are preferable to the employment of non-violent means in the pursuit of their aims.5

For each terrorist, the expected payoff from an attack depends upon: (a) the kind of

attack being attempted (whether N or S); (b) the (anticipated) resistance or deterrence, q,by the immediate victims (e.g., the intended hostages) and the government and security

agencies and (c) the terrorist’s own type, h. For simplicity, we assume that an attack ends

in one of only two outcomes: either success or failure, denoted by the subscripts w and l,

respectively.6

We can write this payoff as:

Euðh; q;NÞ ¼ pwðh; q;NÞ � uwðh; q;NÞ þ ð1� pwðh; q;NÞÞ � ulðh; q;NÞ

where uw(h,q;N ) and ul(h,q;N ) denote the utilities associated with success and failure

respectively. A similar expression, with N replaced by S throughout, characterizes the

expected payoff from a Suicide attack. This general formulation allows for both the

probability of success (failure), and the utility associated with it, to vary with h and q.In order to deal with the comparative statics, and to see the intuition more clearly, we

can simplify this greatly by working with specific functional forms. We start by

normalizing the utility associated with both types of failed missions to 0.7 For the utility

associated with the successful outcomes, we assume that it differs across the different

types h, where 0VhV1, as follows:

uwðh; q;NÞ ¼ eþ kN logðh þ 1Þ

uwðh; q; SÞ ¼ kS logðh þ 1Þ

where kS>kN. We can simplify this, without significant loss of generality, by normalizing

kN to 1, and as a further simplification, set kS=2 and 0<e<log 2. Fig. 1 graphs the utility

functions. The curves can be interpreted as follows: utility from a successful attack is

increasing and concave in h. For low values of h, a Negotiated outcome yields higher

4 It is important to note that the ‘payoff’ to the terrorist comes not from his own death per se, but from the

scale of the death and destruction, with the attendant wide publicity that such an action brings to one’s cause.5 An alternative statement of this is that we are implicitly considering only that portion of the support of the

distribution of h which does not include the ‘peace-oriented’ types. In the next section, where we consider the

likely responses of passengers confronted with an aircraft hijacker, this is a reasonable simplification to make—by

a revealed preference argument, one can conclude that the hijacker has a ‘‘high enough’’ h.6 For the sake of concreteness, it may be helpful to think of the attack under consideration as being the

hijacking of an aircraft, so that N and S correspond to the different objectives of using the passengers as hostages

in bargaining, versus an attack like those of September 11, where the objective is large-scale death and

destruction. In the next section especially, we use aircraft hijacking to motivate the model, but we suggest that the

analysis applies more generally.7 In some sense, we are assuming that a ‘failure is a failure’, regardless of the type of mission. It is possible to

extend the model to show that, so long as the difference in the utility from a failed N mission versus a failed S

mission is ‘‘small’’, then our result still goes through. Details are available from the authors.

u

θ

uw(θ,ρ;N)

uw(θ,ρ;S)

Fig. 1. Utility from a successful attack.


utility than the Suicide outcome—in a sense, only the more ‘fanatical’ end of the hspectrum prefers a successful Suicide attack to a successful Negotiated outcome, in which

their demands are met. We have chosen an extremely simple functional form that

accomplishes this. The log term gives us a concave increasing function. By adding e to

that term in one case, and by multiplying it by a constant greater than 1 in the other case,

we can get differently shaped functions to accord with the intuition described above.

For the probability of success, again, we choose extremely simple specifications. The

respective probabilities of success can be written as:

pwðh; q;NÞ ¼ 1� q

pwðh; q; SÞ ¼ 1� cq

where 0VqV1 and 0<c<1.In both cases, we assume that the probability of success is declining in q, i.e., in the

resistance faced from the passengers, aircrew, etc., as well as the deterrence from the

security agencies, etc. However, this decline is more gradual for the Suicide attackers than

the Negotiators—for example, this might be because Suicide attackers are far more willing

to kill passengers who resist than are terrorists who intend to use the passengers as

bargaining chips in their negotiations. Further, the probability of success is always higher

in a suicide attack—as Sprinzak (2000) suggests, suicide attacks are easier to plan and

execute, and therefore harder to guard against, partly because they do not need a

complicated escape route or rescue operation. Nor do they need the same level of

operational support during the course of the attack itself—for example, to guard hostages

in the case of Negotiations. However, as we see below, the fact that the likelihood of

success in a suicide attack dominates that from the N tactic, does not imply that the S tactic

will always be chosen.


Combining the probabilities and the utility expressions above, we can write:

Euðh; q;NÞ ¼ ð1� qÞ � ½eþ logðh þ 1Þ�

Euðh; q; SÞ ¼ ð1� cqÞ � ½2logðh þ 1Þ�

We are now in a position to define h*, the terrorist who is just indifferent between N

and S, with h<h* favoring the N action, while those for whom h>h* will favor S. Since we

let h range between 0 and 1, thus h* is simply the proportion of terrorists who undertake

the N action, or (the interpretation we use in the next section) 1�h* is the probability that aterrorist is a Suicide attacker.

This leads immediately to our first proposition.

Proposition 1. h*(q) is decreasing in q.

Proof. To find h*, for a given q, set:

ð1� qÞ � ½eþ logðh þ 1Þ� ¼ ð1� cqÞ � ½2logðh þ 1Þ�

Zð1� qÞ � eþ ð1� qÞ � logðh þ 1Þ ¼ ð2� 2cqÞ � logðh þ 1Þ

Zð1� qÞ � e ¼ ½ð2� 2cqÞ � ð1� qÞ� � logðh þ 1Þ

Zð1� qÞ � e ¼ ð1þ q � 2cqÞ � logðh þ 1Þ

Zð1� qÞ � e

1þ q � ð1� 2cÞ ¼ logðh*þ 1Þ 5

Note that log (h*+1) is increasing in h*, and the partial derivative of ((1�q)�e)/(1+q�(1�2c)) with respect to q is given by [�e � ½1þ q � ð1� 2cÞ� � ð1� 2cÞð1� qÞ � e�=½1þ q�ð1� 2cÞ�2 ¼ [ �e� ð1� 2cÞ � e�=½1þ q � ð1� 2cÞ�2 ¼ 2eðc � 1Þ=½1þ q � ð1� 2cÞ�2 ,

which is negative, since c<1. Hence, by the implicit function theorem, h*(q) is decreasingin q. 5

Fig. 2 shows this graphically. An increase in q causes the expected utility from both

courses of action to fall, so that the type associated with the terrorist who is just on the

margin between choosing N and S falls from h1* to h2*.In other words, an increase in q leads the mix of terrorists to change, so that the

likelihood of the Suicide action being favored goes up. As mentioned above, if we

interpret h*(q) simply as the proportion of terrorists choosing the Negotiate option, then

that proportion falls as q rises. Note that when q=1, i.e., when the level of deterrence and

resistance is highest, then h*=0, i.e., only suicide missions are launched. At the other

extreme, when q=0, then h* is at its highest, (close to 1 as e approaches log 2), so that

(almost) all terrorists would choose to take the N action. Note that the expected utility from

both courses of action falls as q rises, since ceteris paribus, the probability of success (from

each course of action) falls. This is perfectly intuitive—attacks of both kinds become less

attractive to terrorists when greater resistance is anticipated. Hence, our model suggests

Increase in ρ

Increase in ρEu

Eu(θ,ρ;N)

Eu(θ,ρ;S)

θθ1 *θ 2 *

Fig. 2. Expected utility of N and S attacks.


that although the number of both kinds of attacks is likely to drop, the proportion of

extremist terrorists is likely to rise as q rises.

It is important to note that, in the analysis above, we have used specific functional

forms, chosen to accord with our intuition about the likely shapes of the relationships they

capture. Hence the insight offered by the model above, that the mix of terrorist actions

might shift adversely as the level of resistance and deterrence goes up, should be viewed as

suggestive but not conclusive. In particular, the formulations of the success probabilities

play an important role, while the assumptions about the utility functions are relatively

innocuous. We develop some intuition for this below.

Define DENS(h,q) as the difference in expected utility between the N attack and the S

attack, i.e., as Eu(h,q;N)�Eu(h,q;S)=pw(h,q;N)�uw(h,q;N)�pw(h,q;S).uw(h,q;S), so that h*is defined by DENS(h*,q)=0. Then, dh*=dq ¼ �½AðDENSðh*; qÞÞ=Aq�=½AðDENSðh*; qÞÞ=Ah*� , which is negative (positive) iff the numerator and the denominator have the same

(opposite) signs.

The intuition for the sign of the denominator is relatively straightforward. The

denominator is negative (positive) if, for a given level of q, the expected utility from the

N attack, relative to the S attack, is lower (higher) for higher h types of terrorists. In other

words, are higher h terrorist types more likely to find the Suicide attack attractive (or at least

less unattractive, if uw(h,q;S)<uw(h,q;N))? Given the way that we have defined h, as themore sanguinary type, it seems only natural to assume that this should be so, i.e., that the

denominator is negative.

The sign of the numerator is less obvious. As q rises, the expected utility from both kinds

of attacks falls, but the sign of the numerator depends on whether the fall in expected utility

from the conventional attack is greater than that from the suicide attack for the marginal type

h*. In the analysis above, this is true, but what makes the intuition for this less obvious, and

more subtle, is that this need not be true for all h types, but only at the margin, for the terrorist


type h* defined by DENS(u*,q)=0. Here, our assumptions that the success probability of the

suicide attack is higher, and is less sensitive to the level of q, are crucial although neither

assumption is decisive.8 For the reasons discussed earlier, these assumptions appear

reasonable to us—more so than the opposite extreme, in which seizing hostages for

Negotiations is ‘easier’, and less sensitive to q, than a suicide attack. Nevertheless, at least

for the sake of completeness, it is important to keep in mind that the analysis above has

focused on the more intuitively appealing case.

3. Information, coordination and mass terror

In order to focus more on the incentives of terrorists with differing motives to choose

particular kinds of attacks, we deliberately ignored the important issue of coordination—

e.g., among the adversely affected parties, such as potential victims, the security agencies,

governments, etc. This omission is potentially important, since one of the more striking

aspects of acts of terrorist-hijacking is the ability of a small set of individuals to hold a

large number of individuals hostage. Indeed in many such situations, it is quite clear that

if all the hostages/victims coordinated their resistance to the hijacker-terrorist, then they

are likely to be successful in frustrating the hijacker-terrorist. Given the potentially large

gains from coordination, it is particularly important to understand the reasons for the

observed coordination failures. In this section we dissect this issue and propose a

remarkably simple policy intervention that can serve as a coordinating device. At the

outset it is important to emphasize that while our analysis focuses on a very simple

stylized hijacker-terrorist example, the analysis is of much more general relevance.9

Indeed our analysis throws light on the role of public pronouncements, and of common

knowledge in achieving coordination of anti-terror operations, not just across individuals

but also countries and their security forces.

As discussed in the previous section, the course of action chosen by the terrorist is either

S or N (we can loosely refer to this as the ‘type’ of the terrorist). We begin by taking the

proportion of ‘suicide’ terrorist-hijackers as given, and consider the likely responses of the

passengers.10 Further, without loss of generality, our analytics will focus on coordination

amongst two passengers or potential hostages—each with preferences given by: uj=0 for

lj<1 and uj=Dj for lj=1, where ja{A,B} represent the passengers and lj<1 is the possibility

that the hostage loses his life due to the terrorist action. We allow each hostage to choose

from one of two actions—they can either choose to cooperate/comply with the terrorist

8 This can be seen by writing out the numerator as: ½Bpwðh*;q;NÞ=Bq�uwðh*;q;NÞ � ½Bpwðh*;q; SÞ=Bq�uwðh*; q; SÞ, and noting that (i) (Bpw(u*,q;N))/Bq and (Bpw(u*,q;S))/Bq are both negative but the former is larger in

magnitude, because the success probability of a suicide attack is less sensitive to q; and (ii) uw (h*,q;N)>uw(h*,q;S), because h* is defined by pw(h*,q;N)�uw(h*,q;N)=pw(h*,q;S)�uw(h*,q;S), and pw(h*,q;N)<pw(h*,q;S). Notethat neither (i) nor (ii) is either necessary or sufficient.

9 As pointed out by a referee, while the example is described in the context of an aircraft hijacking, the

insights can be applied more generally to the analysis of coordinated responses to crimes (for example, on

passengers using public transport) when there is a possibility that security personnel are around.10 For simplicity, we combine all the adversely affected parties, e.g., the passengers, aircrew, air security

officials, etc., under the rubric of ‘‘passengers’’.


(aC), or they can choose to resist (aR). The key assumption that we make is that the hostages

will be successful in resisting and overthrowing the hijacker if and only if they both decide

to resist the hijacker, otherwise they will meet with zero probability of success.11 Table 1

captures the relevant payoffs.12 We now delineate the structure of the game.

On being taken hostage, the passengers have a simple decision to make simultaneously

and independently—whether to cooperate with the hijacker-terrorist or whether to resist.

Observe first that the utility functions are such that if the hijacker-terrorist was known to

be a ‘negotiator’, then the unique equilibrium under weak dominance is for each hostage

to cooperate with the terrorist, since the hostage strictly prefers to live. In contrast, if the

terrorist is known to be on a suicide mission, then (using strict dominance) we have a

unique equilibrium where the hostages prefer to resist, since then (with some probability)

they manage to successfully overpower the terrorist. However, what makes decision

making difficult for the hostage is that the ‘type’ or intent of the terrorist is not known.

Given that lack of information, we can analyze the strategic dilemma faced by the hostages

in the form of a simple Bayesian game, where the common prior amongst the passengers

that the terrorist-hijacker is on a suicide mission is hs.13 This gives rise to the payoff

matrices in Table 1.

Observe that these payoff matrices describe a simple coordination game. There are two

Bayesian Nash equilibria: if the hostages believe that the other hostages are going to resist,

they will all choose to resist; in contrast, if the hostages believe that the others are going to

cooperate with the hijacker, they too will strictly prefer to cooperate. In addition, the

coordination failure equilibrium where the hostages prefer to cooperate with the hijackers is

possibly more likely to arise when the number of agents (i.e. hostages) across whom

coordination has to be ensured goes up.14 Finally, there is the issue of common knowledge

of the parameters underlying the game, which forms an additional factor that is further likely

to result in coordination failure. In particular, the absence of a ‘visible’ event, such as the

September 11 attacks, may result in each hostage believing that the other hostage may

believe that hs equals zero, and hence is unlikely to choose to resist, since for such a playerthe dominant strategy is always to cooperate. Therefore, ‘visible’ terrorist attacks by making

common knowledge the fact that hs is positive, give rise to the possibility that coordinated

resistance by the hostages takes place. However, the actual equilibrium remains indeter-

minate, and we have no way of pinning down which of the two equilibria is more likely.

11 This assumption is stronger than is necessary for our results. All that is crucial for our results is the

assumption (as in the earlier section) that the probability of success is an increasing function of the number of

hostages who simultaneously choose to resist.12 In Table 1, and in what follows, we make a number of simplifying assumptions that are stronger than

necessary to establish our results. For example, in Table 1, we have assumed that the passengers’ payoff from

coordinated resistance against a suicide hijacker is the same as that against a ‘negotiator’ hijacker. This simplifying

assumption can be relaxed without qualitatively affecting the analysis. Details are available from the authors.13 For clarity of exposition, we use hs to denote the perceived probability assigned by the passengers to the

event that the terrorist is a suicide terrorist. This is to distinguish it from the actual proportion of suicide terrorists,

which is 1�h* in terms of the notation of Section 2. Of course, in equilibrium, the beliefs held by the passengers

will be borne out, so that 1�h*=hs in equilibrium.14 However, in order to make this point in a more systematic way we would need to considerably augment

the existing framework.

Table 1

B

(a) ‘Negotiator’ as Hijacker-Terrorist (1�hs)aC aR

A aC DA, DB DA, 0

aR 0, DB DA, DB

(b) ‘Suicide’ Hijacker-Terrorist (hs)aC aR

A aC 0, 0 0, 0

aR 0, 0 DA, DB


Suppose now that the government decides to introduce sky marshals in order to prevent

hijackings. Such a policy intervention by the government, while likely to be effective in

reducing the number of hijackings, is also very costly. However, we now demonstrate a

striking result—the public announcement of government legislation that introduces even a

small percentage of sky marshals to fly on planes would dramatically narrow the set of

parameters for which multiplicity of equilibria holds—so that there exists a unique

equilibrium where the hostages endogenously coordinate their actions and successfully

overthrow the hijacker-terrorist, even if there is no sky marshal around.15 The precise

structure of payoffs generated by the preferences of the hostages in the presence or absence

of sky marshals is captured in Table 2, which is a slightly modified version of Table 1. The

modifications reflect the fact that (i) the sky marshal’s preferences are assumed to be slightly

different from those of the typical hostage—in particular, the sky marshal strictly prefers

resistance;16 and (ii) the probability that there is a sky marshal on board is p.17 If the skymarshal acts alone then he is successful with probability p, where pa[0,1), in which case he

obtains utility DM.

As described above, hostage A can choose from the set of strategies {aC,aR}, while for

hostage B, a pure strategy is one of the four pairs generated by AHAM, where Aj is the set of

actions available to player/hostage B of type tB( j)a{tB(H), tB(M)}, where tB(H) and tB(M)

denote a Player B of type ‘ordinary hostage’ and ‘sky marshal’, respectively. In what

follows we describe the Bayesian Nash equilibria to the game described above. If the

probability that player B is a sky-marshal is below a certain threshold, we have the

possibility of two pure-strategy Bayesian Nash equilibria, in one of which the hostages

always resist. If the probability of player B being a sky-marshal is high enough, then there is

the possibility of a unique equilibrium, where the hostages offer coordinated resistance.

15 The closest analogue to the intuition underlying our model is that in Morris and Shin’s (1998) model of

currency crises. We discuss the parallels and differences between the two models in more detail below.16 In the analysis that follows, the sky marshal always prefers to resist and prevent a hijacking by assumption.

This simplifying assumption captures the general idea that the sky marshal (like firefighters, policemen and

soldiers) is trained always to prefer resistance to passive compliance. The precise channel through which this is

accomplished—whether by special training, or access to weapons or indeed differences in preferences—is not

central to our analysis.17 For simplicity, the notation in Table 2 assumes that passenger B is the possible sky marshal. We ignore the

possibility that both passengers may be sky marshals.

Table 2

(a) Game without Sky Marshal (1�p)tB(H)

aC aR

A aC (1�hs)DA,(1�us)DB (1�hs)DA, 0

aR 0, (1�hs)DB DA, DB

(b) Game with Sky Marshal (p)tB(M)

aC aR

A aC (1�hs)DA, 0 (1�hs)DA+hspDA, hspDM+(1�hs)pDM

aR 0, 0 DA, DM


Proposition 2. There are two pure-strategy Bayesian Nash equilibria whenever pVp* or

equivalently hsVhs*. In the first, A chooses aC while B chooses the strategy (aC,aR), while

in the second A plays aR while B plays (aR,aR). If p>p*, or equivalently hs>h*, then we

have a unique equilibrium in which A plays aR and B plays the strategy (aR,aR).

Proof. We begin our analysis by evaluating hostage A’s optimal strategy under the

assumption that B’s optimal strategy is to resist the terrorist-hijacker irrespective of type

i.e., B chooses (aR,aR). Observe that since the expected payoff to A from choosing to resist

and playing aR equals (1�p)DA+pDA=DA and the expected payoff from aC equals

(1�p)(1�hs)DA+p [(1�hs)DA+hspDA], we have aR as a best response iff,

DAzð1� pÞð1� hsÞDA þ p½ð1� hsÞDA þ hspDA�Z1

pzp

Observe that since p<1, the above inequality holds bpa[0,1], thereby implying that there

exists an equilibrium in which the hostages coordinate and resist the hijacker-terrorist

regardless of their information.

Now consider the pure strategy Bayes–Nash equilibrium when hostage A plays aC and

B plays (aC,aR). Observe that the expected payoff for A from aC equals,

ð1� pÞð1� hsÞDA þ p½ð1� hsÞDA þ hspDA�In contrast, if hostage A plays aR, he obtains,

ð1� pÞ0þ pDA

This implies that aC is a best response if the following inequality holds,

ð1� pÞ½ð1� hsÞDA� þ p½ð1� hsÞDA þ hspDA�zpDA

Simplifying, we obtain a simple condition that aC is a best response for hostage Awhen

B plays (aC,aR) so long as,

p* ¼ ð1� hsÞ½1� hsp�

zp:

Since pa[ 0,1), we always have p*a[1�hs,1). This suggests that so long as p*zp, wehave two pure-strategy Bayesian Nash equilibria—one in which (aC,aR) is an equilibrium,


and the other in which (aR,aR) is another equilibrium. Equivalently, we have two pure-

strategy Bayes–Nash equilibria for hs*zhs, where hs*=(1�p)/(1�pp). Further it is easy to

check that for p>p* , there is a unique equilibrium where A plays aR and B plays

(aR,aR) 5

Observe that the unique equilibrium, where the hostages resist, is guaranteed, even if

none of the hostages is a sky marshal. More strikingly, even if there is ‘mutual knowledge’

(see Osborne and Rubinstein, 1994) that none of the other hostages is a sky marshal, so

long as this fact is not common knowledge, there will be coordinated resistance in the

unique equilibrium. For instance, hostage Awill choose aR, even if he knows that hostage

B is not a sky marshal. This might happen if hostage A believes that hostage B believes

that hostage A believes that B is a sky marshal, and will therefore choose aR.

Therefore, the existence of sufficient uncertainty about the beliefs held by other players

may be sufficient to generate a unique outcome in a coordination game.18 The closest

parallel to this intuition is Morris and Shin’s (1998) model of currency crises, where ‘almost

common knowledge’ about an economy’s fundamentals can generate a unique ‘currency

attack’ equilibrium, even when each currency speculator knows individually that the

economy’s fundamentals are sound.19 The key difference is that, in ourmodel, the possibility

that one of the passengers might be a sky marshal injects uncertainty into the payoffs of the

hostages. By contrast, the closest parallel to Morris and Shin’s (1998) model would be to

have two identical hostages, each of whom receives a noisy signal about the ‘fundamen-

tals’—say, the strength of the hijacker.20 If the hijacker were perceived as weak (strong), then

all the hostages would resist (not resist). And, in the intermediate range, the uncertainty

about the signals received by other hostages would lead to a unique equilibrium with all

hostages choosing to resist.21 By contrast, we are interested in considering the implications

of the possibility of a skymarshal being on board, and how this changes the potential payoffs

of the passengers, as in Table 2. And as we show above, if the possibility that there is indeed a

sky marshall on board is high enough, (i.e., that p>p*), then the multiplicity of equilibria

disappears. Analogous to Morris and Shin (1998), our model demonstrates that the

introduction of uncertainty in the environment can help to eliminate the multiplicity of

equilibria, but where the uncertainty in their model concerned the ‘fundamentals’ of the

economy, in our model the introduction of sky marshals injects uncertainty regarding the

payoffs of each of the hostages.22

18 The fact that a ‘small’ amount of uncertainty can dramatically alter equilibria, was first pointed out by

Rubinstein (1989), and is further explored in Morris and Shin (1997).19 In that model, each currency speculator independently receives a noisy signal about the fundamentals of

the economy. If the fundamentals are ‘weak’ (‘strong’), then there is a unique equilibrium in which the speculators

attack (do not attack) the currency. However, if the fundamentals are in the intermediate range, then there may be

multiple equilibria, in which the speculators attack or not, depending on their perception of what the other

speculators are doing. Morris and Shin (1998) show that, if the true state of the world (‘fundamentals’) is not

known, then uncertainty about the signals received by others might cause all speculators to attack, so that the

multiplicity of equilibria in the ‘intermediate region’ disappears.20 Note that this would be distinct from whether the hijacker is a suicide terrorist or not.21 Loosely speaking, this is analogous to the game described in Table 1, with no sky marshal, but with the

addition of independent signals about the fundamentals (i.e., strength) of the hijacker, to each of the passengers.22 We are grateful to an anonymous referee for helping us to distinguish these insights more clearly.


In our example, the government by making a public announcement about the introduc-

tion of sky marshals in some flights, injects strategic uncertainty, a remarkably effective

policy intervention, which forces potential hijackers to consider the fact that they are likely

to face coordinated resistance. Of course, for this coordinated response to come about, hsmust be positive and common knowledge—something we can reasonably assume is

achieved by events of mass terror such as those of September 11. Moreover, also observe

that, for a given p, if it were perceived that hs had increased sufficiently (say because of thereasons analyzed in Section 2), that would also be sufficient to generate a unique

equilibrium in which the hostages coordinated their resistance against the hijacker-terrorist.

The above example is simplified and ignores important considerations relevant to

effective policy intervention. However, it throws light on an important policy issue for

effective anti-terror legislation. In particular, policy makers have worried about the costs of

effective security measures to prevent (among other things) airline hijackings. Indeed, it is

frequently argued that, given the volume of air travel in the U.S., it is infeasibly expensive to

have sky marshals on every flight. Our analysis says that once we take into account ‘almost

common knowledge’ considerations, a public announcement of the introduction of sky

marshals in some flights would be a very effective policy measure.23 Remarkably, this

policy intervention would be effective even if only a small fraction of the flights had sky

marshals. This is because passengers will offer coordinated resistance and choose aR not

only in the absence of any sky marshals, but even when they are aware that a sky

marshal is not on the flight.

While our analysis suggests that public announcements play an important role in

coordinating actions, we should be cautious and re-emphasize that our analysis is best

treated as a first step. This is especially true not just because our example was highly

stylized, but also because we have neglected other important aspects of public warnings

and terror alerts. Nevertheless, we believe that further exploration of issues of information,

common knowledge and coordination, in the nascent literature on the economics of

terrorism, may have potentially large payoffs.

4. Conclusion

We have analyzed some implications of visible, discrete, large-scale terrorist actions,

such as the September 11 attacks. By making common knowledge the fact that terrorists are

willing to commit suicide, such events of mass terror have direct implications on both the

supply side of terrorism as well as the response to it. First, this paper has presented results on

the implications of increased anti-terror operations on the quantity as well as the mix of

terrorists supplied by terrorist organizations. We find that while the level of terrorist

incidence may decrease, the mix is likely to worsen, with a greater proportion of suicidal

terrorist attacks.24 Second, we also present a novel argument for the role of public

23 Obviously, for the policy to be effective, the precise flights would not be identified.24 Hence, somewhat paradoxically, it may be ‘safer’ to fly after the September 11 attacks than it was before,

in the sense that the likelihood of hijackings declines. However, as Sandler and Enders (2004) speculate,

consistent with the predictions of our model, terrorist attacks are more likely now to be low probability but high

fatality events.


announcements in endogenously coordinating responses in the face of a terrorist-hijacking.

Public announcements, by injecting strategic uncertainty, can give rise to a Pareto-superior

outcome, at minimal resource cost to the government.

An appealing aspect of our analysis is its simplicity. Nevertheless, it is important to

emphasize that our results should be treated as no more than a first step. There are several

directions which deserve to be explored further. First, we would like to have a more

comprehensive general equilibrium analysis of the set of constraints and opportunities

facing terrorist organizations. Indeed such an analysis will give us a better understanding

of how seemingly irrational ‘suicide’ terrorists are very rational in the pursuit of their aims

(see Sprinzak, 2000, for a discussion). Furthermore, such an analysis will throw light on

the effectiveness of alternative measures of combating terrorism. Second, we would like to

further explore the role of common knowledge and public announcements in combating

terrorism. While our example was stylistic and context-specific, it is perhaps a useful first

step in the analysis of the role of public ‘warnings’ and terror alerts—so ubiquitous after

September 11.

Acknowledgements

A previous version of this paper was presented at the workshop on ‘‘The Economic

Consequences of Global Terrorism’’, 14–15 June 2002, DIW Berlin, Germany. For helpful

comments and discussions, we are grateful to Simon Anderson, Albert Choi, Maxim

Engers, Sumit Joshi, Sandeep Kapur, participants at the workshop, and especially our

discussant Todd Sandler. For very helpful discussions and assistance, we are grateful to

Elio Valladares. The detailed comments of two anonymous referees and the editors of this

issue, especially Tilman Brueck, have significantly improved the content and exposition.

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The economics of high-visibility terrorism

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