Terrorism and its oxygen: a game-theoretic perspective on terrorism and the media

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    Terrorism and its oxygen: a game-theoretic perspective on terrorism andthe mediaChristoph P. Pfeiffer aa Department of Economics , University of the Federal ArmedForces , Hamburg , GermanyPublished online: 25 Jul 2011.

    To cite this article: Christoph P. Pfeiffer (2012) Terrorism and its oxygen: a game-theoreticperspective on terrorism and the media, Behavioral Sciences of Terrorism and Political Aggression,4:3, 212-228, DOI: 10.1080/19434472.2011.594629

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  • Terrorism and its oxygen: a game-theoretic perspective onterrorism and the media

    Christoph P. Pfeiffer

    Department of Economics, University of the Federal Armed Forces, Hamburg, Germany

    (Received 3 January 2011; final version received 2 June 2011)

    The symbiotic relationship between terrorism and the media is widely taken as self-evident; theoretical analysis from an economic perspective is rare. In this paper, agame-theoretic model with two players the media and a terrorist organization isdeveloped and then extended to multiple terrorist groups. The number of terroristgroups is first modeled exogenously and then, in a market entry game,endogenously. It can be shown that media attention not only encouragesterrorism, but also has a stabilizing effect. With increasing terrorism and constantmedia preferences, the probability that a single terrorist incident is reported ondiminishes, reducing the expected payoff from a successful terrorist attack.Hence, terrorist attacks of a single group are declining in the overall number ofterrorist groups. Predictions are made about which circumstances encouragemarket entry of terrorist groups. It is found that religiousness, popular supportand, inversely, the national income of the base country, will, ceteris paribus,lead to an increase in potential terrorist groups engaging in terrorism.

    Keywords: terrorism; media; game theory; economics

    The only thing we have to fear is fear itself. (Franklin Roosevelt)

    Introduction

    After the terrorist attacks on 11 September 2001 and the subsequent war on terror, ter-rorism received increased attention from all sides of social science. Economics was noexception. With its focus on preferences and individual choice, economic analysisbegins with identifying terrorists motivation.

    Terrorism can be seen as a special form of political participation, which is ultimatelyaimed at the redistribution of power, property rights and the extortion of rents (Frey &Luechinger, 2002). Schelling (1991) argues that the main tactical goals of internationalterrorism are

    (1) gaining publicity and media attention;(2) destabilizing the existing policy; and(3) damaging the economies of targeted countries.

    ISSN 1943-4472 print/ISSN 1943-4480 online

    # 2012 Society for Terrorism Researchhttp://dx.doi.org/10.1080/19434472.2011.594629http://www.tandfonline.com

    Email: christophpp@gmail.com

    Behavioral Sciences of Terrorism and Political AggressionVol. 4, No. 3, September 2012, 212228

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  • Becker (1968) was the first to analyze criminal behavior in a rational choice frame-work. He argues that criminals respond to incentives just as any other individual andcan be deterred by a higher probability or a greater severity of punishment. With agiven punishment, the probability of capture has to be just high enough to render theexpected net benefit of the crime negative in order to deter criminals.

    The assumption of rationality is essential to economic models. However, the degree ofrationality imposed on economic agents varies. While Mises (1949, 2007) defines humanaction as always rational, the rationality assumption usually rests on further conditions.Rationality in a still relatively thin sense implies that individuals behave consistentlyaccording to their preferences and respond to price changes. Conditions for rationality ina thicker sense include a neither altruistic nor malevolent utility function (narrow self-inter-est), expectations about the future that are correct on average (rational expectations) orknowledge about other individuals utility functions (common knowledge of rationality).

    Rational choice models have been criticized as unrealistic (e.g. Sen, 1977).Examples of individuals not behaving in accordance with the homo economicushypothesis abound; in experiments and in real life, individuals often violate basic prop-erties of rationality (Klein, 2001; Selten, 1991). The idea of bounded rationality can beseen as an attempt to reconcile descriptive and normative decision theory (Gigerenzer& Selten, 2001). While optimization under time and information constraints runs intosimilar theoretical problems as unbounded optimization, Todd (2001) argues that fastand frugal heuristics often produce decisions that are surprisingly close to the optimum.

    How accurate is the rationality hypothesis with respect to terrorism? In order toevaluate terrorists rationality, it is useful to distinguish between different kinds of ter-rorists. Terrorists face different levels of risk exposure, ranging from a sympathizerconfronted with little risk to the suicide bomber facing death almost certainly(Caplan, 2006). Iannaccone (2006) points out that the ex-ante risk of an individualjoining a terrorist organization is probably comparable to that of a person joining thearmed forces; only when assigned certain tasks does the risk increase substantially.

    Following Olsons (1971) theory of collective action, a terrorist organization can beseen as a club (e.g. Berman, 2009; Iannaccone, 2006). Olson (1971) points out that clubmembers have an incentive to free ride off other members contributions. The collectiveaction problem consists of aligning individual rationality with the clubs goals. Becauseof the (extremely) high expected costs involved in conducting terrorist attacks, movingmembers to action is particularly difficult for terrorist organizations. Therefore, the questionabout terrorists rationality leads to a question about incentives: how are terrorists induced tocarry out dangerous tasks? Standard strategies include demonizing the enemy and estab-lishing a sense of moral conviction and strong camaraderie among the terrorists. Therational sacrifice perspective, on the other hand, focuses on immaterial and materialrewards terrorists or their families receive before and after the mission (Iannaccone, 2006).

    Suicide terrorism while from the terrorist organizations point of view a highlyeffective weapon (Pape, 2003; see also Berman & Laitin, 2005) seems to be particularlyantithetic to rationality. How can a person who sacrifices her own life be rational andself-interested? Harrison (2006) explains this apparent paradox by describing suicide terror-ism as a trade of life for the identity of a living martyr. Azam (2005) argues that suicideterrorism is an intergenerational investment. Caplan (2006) concludes that aligningsuicide terrorism with the notion of rationality is probably only possible when includingevolutionary aspects of self-interest as put forward by Dawkins (1976/2006). Overall,while not all terrorists adhere to narrow self-interest, there is empirical evidence that terroristorganizations respond to price changes, such as target hardening or better security measures

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  • (Berman & Laitin, 2005; Enders & Sandler, 1993; Sandler & Siqueira, 2006), renderingBeckarian deterrence and other means of shaping terrorists incentives viable (for an exten-sive review of the economics of (counter-)terrorism see also Schneider, Bruck & Meierieks2010a, 2010b). With reference to the analysis of conflict, Schelling (1960/1980) argues inthe defense of the rationality assumption:

    [W]e seriously restrict ourselves by the assumption of rational behavior not just intelli-gent behavior, but of behavior motivated by conscious calculation of advantages, a calcu-lation that in turn is based on an explicit and internally consistent value system. [. . .] Theadvantage [. . .] for theoretical development is not that, of all possible approaches, it isthe one that evidently stays closest to the truth, but that the assumption of rational behavioris a productive one. It gives a grip on the subject that is peculiarly conductive to the devel-opment of theory. It permits us to identify our own analytical processes with those of thehypothetical participants in a conflict; and by demanding certain kinds of consistency inthe behavior of our hypothetical participants, we can examine alternative courses of behav-ior according to whether or not they meet those standards of consistency. The premise ofrational behavior is a potent one for the production of theory. (p. 4)

    Schelling (1960/1980) also points out that irrationality can, in certain situations, bea strategic advantage. Believing in an irrational ideology, with ideas that are objectivelynot true, can be seen as a suspension of rationality that allows commitment to a certaincourse of action. Osama Bin Ladens claim we love death (Stengel, 2001) could beseen as an attempt to signal an extreme, arguably irrational, preference for conflict,that, if true, would make deterrence by the threat of conflict impossible.

    The media are essential to terrorism; they allow terrorists to scale up intimidation ata low cost. In a recent study, Melnick and Eldor (2010) find that terrorists in Israel areprovided with media coverage free of charge that is on average worth NIS 0.38 millionper incident. The economic damage, measured by a decline in the Tel Aviv StockExchange, increases monotonically with the extent of media coverage. Without thepossibility of receiving public attention, terrorism, as symbolic violence, can qua defi-nitionem not exist. Its goal is to install fear beyond that of the immediate victim(Sandler & Arce, 2007, p. 778). Margaret Thatcher described media attention as theoxygen of publicity on which [terrorists] depend (Apple, 1985, p. A3). Similarly,Laqueur (1976) argues that the media are the terrorists best friend. The terroristsact by itself is nothing. Publicity is all (p. 204).

    While there seems to be unanimous consent about the symbioticity of terrorism andthe media (Hoffmann, 2006), theoretical research on the nature of this relationship israre. To the authors best knowledge, so far there have been two contributions thatanalyze, in a rational choice framework, how terrorists and the media interact.

    Scott (2001) looks at the terrorismmedia interaction as a common propertyproblem in which terrorist groups compete for limited media attention. Because ofconvex preferences of the public regarding terrorist and nonterrorist news and finitepublic attention, more terrorist incidents will lower the coverage per incident. The pro-spect of reduced media attention induces terrorists to lower the equilibrium amount ofterrorism. He finds empirical evidence in support of the hypothesis that an increase interrorist incidents leads to lower media attention per incident.

    Frey and Rohner (2007) have made another interesting contribution proposing agame-theoretic model with a terrorist group and the media as players. Three equilibriaemerge, one of which is unstable and the other two are corner solutions: either no ter-rorism occurs, and consequently there are no news about terrorism, or all terrorist effort

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  • is put into terrorism, and the media report about terrorism only. The problem with mul-tiple equilibria is that it is not clear which equilibrium will be chosen. In order to tacklethis problem, the authors develop a discrete choice model and calculate the conditionsfor a dominant strategy on both sides. Intermediate levels of terrorism are explained byextending the analysis to multiple terrorist groups. Frey and Rohner (2007) find empiri-cal evidence that media attention Granger-causes terrorism and vice versa. Conse-quently, they emphasize the importance of subsidizing high-quality journalism, anonattribution policy and a decentralization of the polity.

    In this paper, a different game-theoretic model is proposed. First, the basic model isset up with two players, a terrorist group and the media, which are viewed as a singleplayer. Both players make their move simultaneously while they cannot communicatewith each other; common knowledge of rationality is assumed. The media maximizetheir utility by determining the probability that a terrorist attack makes it to thenews, thereby implicitly deciding on the fraction of terrorist news relative to othernews. Since the medias preferences are assumed to be constant, an expected highlevel of terrorism, resulting from radical terrorist preferences, will lead to a low report-ing propensity, whereas a low level of terrorism will lead to a high reporting propensity.The terrorist organization has political goals it wants to attain by employing nonviolentpolitical means or terrorism, the expected marginal utility of which is determined by themedias reporting propensity for terrorist incidents. An intermediate, stable Nash equi-librium of terrorism and reporting propensity emerges when both players independentlymaximize their utilities. In the Nash equilibrium, neither player has an incentive to uni-laterally alter her strategy. A level of terrorism that owing to exogenous shocks isabove the equilibrium reduces the medias reporting propensity, which lowers theincentives for the terrorist organization to carry out terrorist attacks, and consequentlythe number of attacks decreases. On the other hand, an initially low level of terrorismleads to a high reporting propensity, increasing the expected benefit from terrorism andhence the number of terrorist attacks. While the media enable terrorism, they also havea stabilizing effect, keeping terrorism from moving to extreme levels.

    In the next section, the analysis is taken one step further with the introduction ofmultiple terrorist groups. The overall number of terrorist groups is given exogenouslywith a single media entity on the other side. More terrorist groups lead to an increase inoverall terrorism. However, the number of attacks conducted by a single groupdeclines. More terrorist groups engaging in terrorism means more competition forscarce public attention. The media keep the share of news about terrorism, accordingto their preferences, constant, and so the reporting propensity per incident declines.The expected benefits of terrorism decrease, and individual terrorist groups decreasethe number of attacks. Terrorist groups crowd each other out because public attentionis limited. If, instead of being utility maximizers, terrorist groups were motivated byaspiration levels, i.e. certain levels of public attention, market entry of other terroristgroups would have the contrary effect: in order to maintain the same level of publicattention, terrorist groups would have to increase the number of attacks. Because offinite public attention, an eventually unsustainable rat race might emerge.

    Finally, the number of terrorist groups is, in a market entry game, modeled asendogenous. When a group considers whether to engage in terrorism, it weighs costsagainst benefits. In the model developed, the benefits a group can expect from conduct-ing acts of terrorism depend on the probability of a terrorist act being covered by thenews. The reporting propensity and hence the expected benefits of terrorism are a func-tion of the number of groups engaging in terrorism. It is argued that the costs of a

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  • terrorist group depend mainly on its resilience. Drawing upon the work of Berman(2009) as well as Jones and Libicki (2008), the expected costs of a group engagingin terrorism are expressed as a function of the groups religiousness, its size and, inver-sely, its base countrys national income. A high number of terrorist groups may determarket entry of other groups; factors that lower the expected costs of terrorism will leadto an increasing number of groups engaging in terrorism.

    The model

    In this section, a simple game-theoretic model is developed. There are two players, a ter-rorist group and the media. The media are seen as a unified entity. Both maximize theirutility while taking the other players actions into account. Terrorists set a certain amountof terrorism while the media decide how much attention they devote to terrorist incidents.Both make their move at the same time and cannot communicate with each other or makeany kind of commitment in advance. It is further assumed that both players have commonknowledge of rationality: either player knows the others utility function and also knowthat the other player knows, and so ad infinitum. In addition, both players are rational andaware of the others rationality. A single stable Nash equilibrium is obtained, in whichneither player has an incentive to unilaterally alter her strategy.

    The terrorist group has political goals, which it tries to achieve by nonviolent meansO, terrorism T, or a combination of the two. It faces the following resource constraint:

    1 = T + O (1)

    In favor of simplicity, quasi-linear utility functions are assumed for the terrorists andthe public. The terrorist groups utility function is given by:

    UT = a pT( )b+O (2)

    where a . 0 is their relative preference for terrorist activity and p 0 the extent towhich terrorist attacks are covered by the media. Terrorists are motivated by the pro-spect of media attention only. Therefore, if the media do not report on terroristattacks (p 0), the marginal utility of terrorism becomes zero, and no attacks occur.The value 0 , b , 1 determines the (decreasing) marginal utility of terrorist attacksthat the media report on. Both T and p are subject to decreasing marginal utility.From the individual terrorists perspective, this seems plausible. Once a certainreputation has been established, the additional gain from further publicity decreases.Substituting equation (1) into equation (2) leads to:

    UT = a pT( )b+ 1 T( ) (3)

    The first-order conditions for maximizing the terrorists utility yield the terroristsreaction function,

    T p( )

    = pbab( )1/ 1b( )

    (4)

    The media can only produce a limited amount of content and so have to choosebetween news concerning terrorism and other news. They decide the amount of terrorist

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  • news indirectly by adjusting the extent p to which terrorist incidents are covered. There-fore, pT is the amount of news about terrorism. With F as the amount of nonterroristnews, the medias content restriction can be written as:

    1 = pT + F (5)

    which can be understood as the limited space available in a newspaper or the limitedtime in a newscast. The medias utility function is given by:

    UM = g pT( )d+F (6)

    with g . 0 being the medias relative preference for terrorist news coverage and 0 , d, 1 determining the (decreasing) marginal utility of terrorist news coverage. The prob-ability that nonterrorist events are reported on is not explicitly modeled, althoughcrowding-out effects with other attention attracting events seem likely. Modeling amedia market is beyond the scope of this model, so the medias utility function isassumed to be exogenous.

    Substituting equation (5) into equation (6) yields

    UM = g pT( )d+ 1 pT( ) (7)

    Maximizing Up leads to the medias reaction function:

    p(T ) = (gd)1/(1d)

    T(8)

    which is convex and monotonically decreasing in T (see Figure 1).Given equations (4) and (8), a single stable Nash equilibrium can be derived at:

    T = ab gd( )b/ 1d( )

    (9a)

    p = (gd)(1b)/(1d)

    ab(9b)

    which, geometrically, is the point of intersection of the two reaction curves (see Figure1). The total amount of terrorist news coverage is Tp (gd)1/(1 2 d). In equilibrium, noplayer has an incentive to unilaterally alter her strategy, since any deviation from theequilibrium would lead to a lower utility.

    The model suggests that a high attention incident ratio is unsustainable at highlevels of terrorism because the media only want a certain amount of all news to beabout terrorism. Also, it can help to understand differences in terrorism and reportingpropensity among countries. In a country that experiences higher levels of terrorism,the resulting reporting propensity will, ceteris paribus, be lower than in a countrythat experiences low levels of terrorism (see Figure 1).

    Given that both players have common knowledge of rationality, in a sequentialmove game, without the possibility to make binding commitments, the same Nash equi-librium emerges as in equations (9a) and (9b). This changes if players have to infer the

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  • other players parameter from past observations. If terrorists assume that the mediasreporting propensity of the present period is going to be the same as the reporting pro-pensity in the last period, the number of terrorist attacks begins to fluctuate over time.For a high marginal utility of news about terrorism, the amount of terrorism over time isexplosive; for a low marginal utility of public attention, the amount of terrorism con-verges to the Nash equilibrium (see Appendix A, P1).

    According to the newsworthiness theory, events receive a high level of attentionfrom the media that, among other factors, score high on meaningfulness, proximity,personification, unexpectedness and negativity (Galtung & Ruge, 1965). Terrorismdoes score high on most of these attributes and therefore receives a level of attentionthat is much higher than would be justified by its prevalence. Overreporting maycause news consumers to overestimate the real threat terrorism poses and henceinduce irrational anxiety (see Pfeiffer, Windzio, & Kleimann, 2004, on the effectmedia consumption has on perceived crime rate; see also Slone, 2000 on the anxietyinducing effect terrorist news consumption has). Gigerenzer (2004) calculates thatthe substitution from air to road travel in the year after the terrorist attacks of 11 Sep-tember 2001 led to an increase in the number of fatalities that exceeded the number airpassengers that died on 11 September 2001 owing to the attacks.

    A solution to the dilemma of limiting terrorisms impact while maintaining civil lib-erties can possibly be found in risk education. If an easily understandable measure of riskwas added to all news about terrorism, news consumers might be better equipped toevaluate the actual danger. This may reduce anxiety and hence the impact of terrorism.

    Exogenous number of groups

    While in the previous section the focus is limited to a single terrorist group, in thissection, the model is extended to multiple terrorist groups. With more than one

    Figure 1. The reaction curves of the media p(T) and the terrorists TH(p) and TL(p) intersect atthe Nash equilibria. TH(p) is the reaction function of a terrorist group with a relatively strongpreference for terrorism (aH 0.965) and TL(p) the reaction function of a group with a rela-tively low preference for terrorism (aL 0.433).

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  • group, terrorists compete for scarce media attention. Throughout the paper, it isassumed that competing terrorist groups have different, but nonconflicting goals. Foranalytical purposes, different groups with the same goal could be viewed as single,large groups. Terrorist organizations with the same goals would have an incentive tofree ride off other groups attacks. In contrast, competition between terrorist groupswith opposing goals would be more intense. A terrorist attack of another group withgoals that are in conflict with the groups own goals would have a disutility not onlyby congesting the media, but also from an undesired possible political impact.

    Let n be the number of terrorist groups in the market for terrorism. Assuming hom-ogenous preferences and resources, the utility of a terrorist group i 1, . . ., n is:

    UT ,i = a pTi( )b+Oi (10)

    The media take all terrorist incidents into account:

    Up = g pni=1

    Ti

    ( )d+ 1 p

    ni=1

    Ti

    ( )(11)

    Optimizing both utility functions yields the reaction functions for the terrorist groupsand the media,

    Ti p( )

    = pbab( )1/ 1b( )

    (12)

    p(T ) =gd( )1/(1d)

    ni=1Ti

    (13)

    While the overall amount of terrorism increases in the number of terrorist groups,changes in the amount of overall terrorism will be lower than changes in the numberof terrorist groups engaging in terrorism, e.g. a reduction in the overall number of ter-rorist attacks after counter-terrorism operations may be lower than expected if a linearrelationship is assumed. A reduction in the number of terrorist groups reduces compe-tition. Therefore, the marginal benefit of terrorism increases and induces individual ter-rorist groups to increase their number of terrorist attacks (see Appendix B, P2).

    Since overall terrorism is increasing in the number of terrorist groups, the reporting pro-pensity declines with more terrorist groups. The higher the number of groups that engage interrorism, the lower the attention a single terrorist incident receives (see Appendix B, C1).There is empirical evidence for a crowding-out effect: when the media cover one terroristattack, other acts of terrorism receive less attention (Scott, 2001).

    The amount of terrorism a single terrorist group produces is declining in the numberof terrorist groups (see Appendix B, C2). With more terrorist groups competing forattention, the probability of an incident being covered by the news declines. Thisreduces the marginal expected benefit of terrorism. A rational, utility maximizing ter-rorist group will then decide to reduce terrorism and allocate its resources to activitiesthat have a higher marginal payoff than terrorism. On the other hand, a group motivatedby aspiration levels (i.e. the group wants to maintain a certain level of public attention)

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  • might actually increase the number of attacks it carries out when competition increases.However, attempts to keep its share of news constant would be deemed to fail if com-peting groups were also satisficing. A rat race for public attention would emergebetween the different terrorist groups, leading either to a readjustment of aspirationlevels or possibly ruinous competition.

    Endogenous number of groups

    In order to determine how many groups will engage in terrorism, a market entry gamewith two homogenous players has been developed. A market entry game can be usedto analyze situations in which a number of players have to independently and simul-taneously decide whether to undertake some activity, the utility of which decreaseswith the number of players deciding to undertake it. Examples include entering amarket, driving a certain road by car or applying for a job. In contrast to other coordi-nation games such as the battle of the sexes, an overall maximum utility is not achievedby symmetric, but by asymmetric decisions. While usually monotonicity of externalitiesis assumed, in many situations, net externalities may first be positive, and then, after acertain optimal point is passed, become negative (Anderson & Engers, 2006).

    Out of a population of N potential terror groups, n N will enter the market forterrorism. Group i, i 1, . . ., N can decide to stick to nonviolent political means Oonly, or to enter the market for terrorism and spend its resources on a combinationof terrorism and nonviolent political means. Engaging in terrorism comes at highcosts, individually and at the group level. Becoming a terrorist means having to livewith a substantial risk of prosecution, injury, death or even torture. The prosecutionrisk is likely to last even after the terrorist has stopped engaging in terrorism and somay affect his ability to return to a normal life.

    The costs of engaging in terrorism are summed in the variable Mi (opportunity costsare already taken into account in the original utility function, equation (2)). The utility

    Figure 2. The overall amount of terrorism increases concavely with an increasing number ofterrorist cells. The equilibrium probability of news coverage about a terrorist incident falls withmore terrorist groups. The terrorism of an individual cell is falling in the overall number of cells.

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  • function of group i is a function of the variable wi, wi 0 indicating group i not enter-ing the market for terrorism, and wi 1 indicating its entry:

    UT ,i(w) =1 if wi = 0

    1 + An Mi if wi = 1

    {(14)

    Because of the quasi-linear utility function of terrorist groups (equation (2)) and theresource constraint (equation (1)), investing all resources into nonviolent politicalmeans will simply yield a utility of 1. The utility of engaging in terrorism can beobtained by combining the Nash equilibrium amount of terrorism in a multipleplayer setting (equation (B2)) with the terrorists utility function (equation (2)), deduct-ing the market entry costs Mi. To simplify notation, let A/n = (a(gd)

    b1d(1 b))/n be

    the additional utility a terrorist group receives when engaging in terrorism.Differences in market entry costs among terrorists groups can partly be explained by

    organizational factors. As any other group, terrorists are confronted with organizationalchallenges, such as collective action, shirking and delegation problems. Defectionwithin the organization is one of the most serious threats any illegal organizationfaces: [A] single defector can cause an entire cell to be exposed, probably leadingto the arrest or assassination of all his fellow members (Berman, 2009, p. 17). There-fore, the way a terrorist organization deals with this threat largely determines theirexpected costs when entering the market for terrorism. Radical religious groupsseem to have a distinct advantage over nonreligious groups in their ability to limitdefection, resulting in higher resilience and a higher ability to inflict damage. Aperson that is radically religious has to spend a considerable fraction of her lifetimepracticing religion, which leads to a cultural and human capital that is (a) very special-ized and (b) not transferable, reducing the opportunity costs of not defecting. Radicalreligiousness can hence be used as an auditing instrument that credibly signals commit-ment (Berman, 2009). Other interrelated factors that tend to increase a terrorist groupsresilience are popular support, its ability to attract new members, its size, and (inver-sely) the national income of its base country (Jones & Libicki, 2008). Nonetheless, reli-giousness remains the best predictor for a terrorist groups resilience. Size as apredictive factor, while being correlated with the longevity of terrorist groups, is notincluded in the function because it seems plausible that surviving groups growduring their lifetime, which makes size endogenous to longevity. The groupspopular support is a function of the public goods it provides relative to the publicgoods provided by government. The higher the national income of a country themore public goods it can provide, thereby crowding the terrorist organization out. Inaddition, a country with a high national income can afford better counter-terrorismmeasures. Since the future costs of engaging in terrorism depend largely on a terroristgroups resilience, group-specific market entry costs can be expressed as a function ofits religiousness Ri, the popular support it enjoys Si, and the national income Ij of itsbase country j 1, . . ., Z:

    Mi = Mi Ri, Si, Ij( )

    (15)

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  • with the first partial derivatives being

    MiRi

    , 0,MiSi

    , 0,MiIj

    . 0 (16)

    In a population of two potential terrorist groups, N 2 and symmetrical entry costs, Mi M, i 1,2, the payoff matrix can be written in the normal form (Table 1).ENTER indicates a groups strategy to enter the market for terrorism, ENTER indicatesa groups strategy to refrain from terrorism. The payoff when engaging in terrorismdepends on whether the other player decides to engage in terrorism as well, since theprobability of news coverage, and hence the expected utility, is lower when there areincidents from other terrorist groups as well. There are four pure-strategy Nash equili-bria and one mixed-strategy Nash equilibrium.

    Which equilibrium emerges depends on the relative size of the market entry costs,M. Two of the pure-strategy Nash equilibria are trivial: for entry costs being sufficientlylow (M , A/2), entering the market is a strictly dominant strategy resulting in bothplayers market entry in Nash equilibrium in S1

    (ENTER, ENTER). For entrycosts being sufficiently high (M . A), not entering is a strictly dominant strategyleading to the second symmetric, pure-strategy Nash equilibrium in S2

    (ENTER,ENTER). When market entry costs are in between the two above cases(A/2 , M , A), there is no dominant strategy, i.e. there is no strategy that is alwaysoptimal, regardless of the strategy of the other player. This situation is similar to agame of chicken: both players receive their maximum payoff when they enter andthe other player does not enter. Both receive a net disutility when they enter simul-taneously because media attention then has to be shared among them. Both playersnot entering is not an equilibrium because either player could receive a higher payoffby changing her strategy to entering, given that the other players strategy remainsunchanged. Both combinations of one player entering the market and the otherplayer not entering (S3

    (ENTER,ENTER), S4 (ENTER, ENTER)) are Nash-equilibria since none of the players has an incentive to unilaterally alter her strategy.However, it is not clear which of these two equilibria will emerge.

    If within their ability, either player will try to deter market entry of the other, eitherby entering the market first or by committing to market entry and then signaling itscommitment to the other player. Game theoretic learning theory as well as experimentalsetups indicate that, when a market entry game is repeatedly played, players strategies

    Table 1. A player receives the highest payoff when she enters and the other player does notenter. Both players engaging in terrorism at the same time yields an inferior payoff since mediaattention would be higher if they entered at different times.

    Group 1

    ENTER ENTER

    Group 2 ENTER (1; 1) (1; 1 + A 2 M)

    ENTER (1 + A 2 M; 1)1 + A

    2 M ;

    1 + A2 M

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  • tend to converge to an asymmetric pure equilibrium with some players permanently inthe market and some players permanently out (Duffy & Hopkins, 2004).

    Since learning theories take a long-term perspective, players may at first decide torandomize their choice of strategy. The expected number of market entrants can then beshown to depend negatively on the costs of market entry (see Appendix C, P3). Hence,the models predicts that the market entry rate of potential terrorist groups, which can bedefined as N/n, will be higher in an environment with more religious groups, groupsenjoying more popular support and in countries with a lower national income (seeAppendix C, C3). Since the overall level of terrorism is a function of the number ofgroups engaging in terrorism, the factors that contribute to a higher market entry ratewill also lead to an increased level of terrorism. If the game is played multiple timesand if players can communicate with each other, they could coordinate their attacksover time, so that each of them receives maximum attention per incident, therebyincreasing the cost-effectiveness of attacks.

    Summary and conclusion

    The media and terrorists do live in a close relationship. The terrorist organizations abilityto spread fear and intimidation depends on the media to a large extent. While the mediaare extremely useful for terrorists, the attention terrorists can receive through the media isfinite. Thus, terrorists compete for attention with other news, especially with news aboutother terrorist attacks. With a higher level of overall terrorism, a single incident willreceive less attention, which leads to a lower marginal utility of terrorism and conse-quently fewer attacks per group. Therefore, the media have a stabilizing effect on terror-ism. The effect works in both directions: changes in resources or the number of terroristgroups lead to an under-proportional adjustment in terrorism. For example, after success-ful counterinsurgency operations, the level of terrorism may decline less than expected ifa linear relationship is assumed. On the other hand, an increase in the number of terroristgroups leads to a decrease of terrorism per group because terrorists groups anticipate thereduced reporting propensity. This result implies strong rationality. If instead terroristgroups were motivated by aspiration levels, increased competition might induce themto increase the number of terrorist attacks. However, if all players were motivated byrigid aspiration levels, competition would eventually become unsustainable.

    The decision, for an individual or a group, whether or not to engage in terrorismdepends on both costs and benefits. The benefits are a function of the attention theterrorist attacks receive. The attention depends on the amount of other emotionallyrelevant topics and, more importantly, on the number of terrorist incidents fromother groups, since the elasticity of substitution is higher for similar news topics. Ahigh level of terrorism may deter other potential groups from engaging in terrorism. Ifdifferent terrorist groups are able and willing to coordinate their efforts, they willspread incidents over time, so that each incident receives a maximum amount of attention.

    Differences in costs among terrorist groups depend mainly on a groups resilience,for which the best predictive factor is religiousness. Religious terrorist groups are betterequipped to limit defection of their members, the biggest threat illegal organizationsface. Another factor determining a groups resilience is its popular support, whichdepends on the level of public goods it is able to provide to its supporters, relative tothe amount of public goods provided by other sources. The national income of thegroups base country inversely influences a groups resilience. A richer country canspend more money on counter-terrorism and provide more public goods, which

    Behavioral Sciences of Terrorism and Political Aggression 223

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  • lowers the relative amount of public goods provided by the terrorist group and hencethe popular support it receives. A higher resilience implies lower costs for a terroristgroup. It can therefore be concluded that a countrys religiousness, the popularsupport its potential terrorist groups have and, inversely, its national income arefactors that, all other things equal, lead to higher levels of terrorism.

    Some of the models results have been confirmed by other research, others have notbeen empirically evaluated yet. The basic question of whether there is a causal relation-ship between press freedom and the amount of terrorism has not been answered yet,mainly owing to the difficulties in disentangling the underreporting bias present inundemocratic countries from the encouragement effect a higher reporting propensityhas (Drakos, 2007). Other questions open to empirical analysis are: does a highernumber of terrorist groups lead to fewer terrorist incidents per group? Can statisticalinformation reduce anxiety responses in recipients after watching news about terror-ism? Do terrorist groups coordinate their attacks over time?

    Further theoretical analysis could be directed at exploring how terrorist organiz-ations use service provision to secure public support, how attacks are coordinatedover time to attain maximum attention, and how terrorist organizations escalate vio-lence to compete for public attention.

    Notes on contributorChristoph P. Pfeiffer is an intelligence officer in the German Army. He studied economics at theUniversity of the Federal Armed Forces in Hamburg and at the United States Military Academy.He is a PhD candidate in economics (economics of terrorism).

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    Appendix A: Adaptive expectations

    Proposition 1 (P1): If the terrorist group forms its expectations about the medias reporting pro-pensity of the current period, pt, based on the medias reporting propensity of the previousperiod, pt 2 1, terrorism will be eventually oscillate between 0 and 1 for b . 0.5. For b ,0.5, terrorism converges to the two-player Nash equilibrium.

    If the terrorist group forms its expectations about the medias reporting propensity pt of thecurrent period based on the last periods reporting propensity pt21, the terrorist groups reactionfunction for period t becomes

    Tt pt1( )

    = pbt1ab( )1/1b

    (A1)

    The media determine their reporting propensity based on the amount of terrorism in the currentperiod,

    pr (Tt) =(gd)1/ 1d( )

    Tt(A2)

    After substituting equation (1) into equation (2) the first-order difference equation can be solvedfor T(t), yielding

    T (t) = Ab

    b 1

    ( )te

    bb1

    ( ) 1

    ( )((1 d)(ln(a) + ln(b)) + b(ln(g) + ln(d)))

    d 1 (A3)

    with 0 , A , 1 being the terrorists initial amount of terrorism.For b . 0.5,

    limt1 T t( ) = 0, 1 (A4)

    Figure A1. If terrorists have adaptive expectations, the amount of terrorism fluctuates overtime. In case of a relatively low marginal utility of media attention (b , 0.5), terrorism stabilizesover time. In case of a relatively high marginal utility of media attention (b . 0.5), an extremecase emerges with alternating between a maximum amount of terrorism and no terrorism. Thegraph on the left hand side displays the stable case (a 0.549, a 0.845, b 0.484, d 0.314, g 0.48), the graph on the right hand side displays the explosive case (a 0.152, b 0.845, d 0.314, g 0.48).

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    http://www.time.com

  • For b , 0.5,

    limt1 T t( ) = ab gd

    ( ) b1 d. (A5)

    B

    Appendix B: Exogenous market entry

    Proposition 2 (P2): A change in the number of terrorist groups will lead to a change in overallterrorism that is smaller than the change in the number of terrorist groups.

    Because of the terrorist cells homogeneity, equation (13) can be further simpli-fied

    ni= 1 Ti = nT

    ( )leading to a Nash equilibrium:

    p = nb1gd( ) 1b( )/ 1d( )

    ab(B1)

    T = nbab gd( )b/ 1d( )

    (B2)

    which translates into an overall level of terrorism of nT=n1 2 bab(gd)b/(1 2 d). A change in thenumber of terrorist groups hence leads to a change in overall terrorism of(nT )n

    = nbab 1 b( )

    gd( )b/ 1d( )

    . 0

    which is positive for the assumed range for parameters. The second derivative can be calcu-lated to be

    2(nT )n2

    = n1b 1 b( )

    b2 gd( )b/ 1d( )

    . 0 (B3)

    Thus, overall terrorism increases monotonically and concavely in the number of terrorist groupsB

    Corollary 1 (C1): The reporting propensity decreases with the number of terrorist groups.

    p

    n=

    1 b( )

    n2b gd( ) 1b( )/ 1d( ) , 0 (B4)

    Corollary 2 (C2): The terrorism a single group produces declines with the number of terroristgroups.

    T

    n= n1bab2 gd

    ( )b/ 1d( ), 0 (B5)

    Appendix C: Randomized market entry

    Proposition 3 (P3): If terrorist groups decide to randomize their market entry strategy, thenumber of expected market entries depends negatively on the market entry costs.

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  • If group 1 decides to randomize its decision to enter the market, with a market entry prob-ability of Pi = 1 Pi, group 1s expected utility can be written as

    E[UT ,1] = P1 + P1(P2 (1 + a (gd)b

    1d(1 b) M )

    + P2(1 +a

    2b(gd)

    b(1d)(1 b) M ))

    (C1)

    Optimizing the expected utility with respect to P1 yields P2 as a result since the partial derivativeof equation (C1) with respect to P1 does not contain P2. This means that player 1 optimally setsher own probability of market entry so that player 2 optimally chooses her market entry prob-ability to be

    P2 =2b a b 1

    ( ) M gd

    ( )b/ d1( )( )a b 1( )

    2b1( ) (C2)

    Because of symmetricity, it follows that player 2 sets her market entry probability so that player1 optimally chooses

    P1 =2b a b 1

    ( ) M gd

    ( )b/ d1( )( )a b 1( )

    2b1( )

    Hence, S5 = P1 ;P2( )

    represents a symmetrical equilibrium in market entry probabilities. Theexpected number of players that enter the market hence becomes

    E n[ ] = NP =21+b a b 1

    ( ) M gd

    ( )b/ d1( )( )a b 1( )

    2b1( ) (C3)

    with P = P1 = P2. The partial derivative of the expected number of market with respect tomarket entry costs entries can now be calculated to be

    E n[ ]M

    =21+b gd

    ( )b/ d1( )a 2b 1( )

    b 1( ) , 0 (C4)

    B

    Corollary 3 (C3): The expected number of market entries depends positively on the groups reli-giousness and its popular support and negatively on its base countrys national income.

    Given that

    M

    R, 0,

    M

    S, 0,

    M

    I. 0,

    it follows from equation (C4) that

    E n[ ]R

    . 0,E n[ ]S

    . 0,E n[ ]I

    , 0

    B

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