The Paradox of Misaligned Profiling

Abstract

This article implements an experimental test of a game-theoretic model of equilibrium profiling. Attackers choose a demographic “type” from which to recruit, and defenders choose which demographic types to search. Some types are more reliable than others in the sense of having a higher probability of carrying out a successful attack if they get past the security checkpoint. In a Nash equilibrium, defenders tend to profile by searching the more reliable attacker types more frequently, whereas the attackers tend to send less reliable types. Data from laboratory experiments with financially motivated human subjects are consistent with the qualitative patterns predicted by theory. However, we also find several interesting behavioral deviations from the theory.

Keywords

terrorism profiling game theory laboratory experiment

An important problem facing security personnel is to identify terrorists within large groups of mostly innocent people. This problem arises at checkpoints of all kinds, such as roadblocks, permanent checkpoints between different regions or countries, and airport security counters. In such settings, large numbers of people pass through a screening process designed to detect and detain terrorists. Typically, the volume of traffic in comparison with the number of potential terrorists is so large that it is neither economically nor politically sensible to screen everyone with the intensity required to detect a terrorist. The security personnel, therefore, face the difficult task of deciding whom to take out of line and subject to greater scrutiny when there are many innocent people and few terrorists. For instance, this issue was faced at US military checkpoints that attempted to secure the Green Zone in Baghdad during the US occupation, and it is also faced daily at busy airports, especially during periods of high-security alert.

The problem is compounded by the fact that a terrorist group may be strategic in the sense of being able to respond quickly to any targeted screening program. If the government screens one category that is closely associated with the terrorist group (for instance, young men from a certain province in the Iraq case), then the terrorist group faces a strong incentive to begin recruiting and sending people outside that category, for example, women. The government would then rationally respond by searching women, at least to some extent. The equilibrium outcome of this interaction is unclear. Some argue for a completely random search process, but that would give the terrorists an incentive to send only their core supporters, since they would be no more likely to be searched than anyone else, and these core supporters would presumably be more likely to carry out a successful attack if not searched. There is a need for careful analysis to determine what kind of search strategy is rational, implementable, and efficient in an environment with threats that evolve in response to securities measures.

Profiling occurs when a certain characteristic or signal, such as race or ethnicity, is used to decide who to subject to a more intrusive investigation. Racial profiling, for instance, is based on the belief that certain crimes are committed disproportionately by the members of a particular race. The scholarly debate in the social science literature is mostly focused on whether profiling occurs and whether it is effective, rather than on normative and constitutional issues. Profiling is not per se illegal in most countries, and legal scholars have discussed the pros and cons of various types of profiling and the circumstances under which it might be justified (Barnes and Gross 2002; Ellmann 2003).¹ Economists have studied racial profiling issues from the perspective of whether profiling is a rational use of limited enforcement assets. A recent study pioneered by Knowles, Persico, and Todd (2001) has characterized the Nash equilibrium of a simultaneous move game between the police and a specific group of the population, such as motorists/drivers, who may commit a crime. The police objective is to minimize crime when deciding which vehicles to search, while motorists choose whether to carry contraband or not. The equilibrium involves unequal investigation rates across different demographic groups, even if police officers are unbiased, as long as the members of one group incur higher costs of carrying contraband than those of another group. In this sense, profiling can result from a type of rational experience-based or “statistical” discrimination. Antonovics and Knight (2009) point out that if statistical discrimination alone is used to explain differences in the rates at which vehicles of drivers of different races are searched, then these search decisions should be independent of police officers’ own race. They test this prediction using data from the Boston Police Department and find that officers are more likely to conduct a search if the race of the officer differs from the race of the driver.

The debate on profiling significantly changed after the terrorist attacks of September 11, 2001. Screening procedures have included different versions of the Computer Assisted Passenger Prescreening System and the Secure Flight Passenger Screening Program, a computerized tool to select passengers for screening, and more recently the full body image scanning. Passengers with elevated ratings according to these mechanisms are selected for additional searches and for baggage inspection, while some other passengers are still searched at random. If previously the discussion was about whether demographic profiling was happening, after 9/11 researchers and politicians have focused on the conditions under which such profiling is acceptable, either constitutionally or as a policy matter. All screening and profiling mechanisms have encountered criticisms and often legal actions. Computerized searching mechanisms are often accused of inducing racial or religious profiling and discrimination. In fact, there is a debate among experts about whether profiling strategies are more effective than are pure random searches.

Several years ago, on November 22, 2010, National Public Radio held an Oxford-style debate at the New York University with the two teams arguing the motion “Should U.S. Airports Use Racial and Religious Profiling?” Advocates of the motion supported the use of profiling specifically concentrating on young fundamentalist Muslim males from the Middle East, as the majority of recent terrorist attacks have been associated with this type of individual. Opponents argued that profiling just invites terrorist groups to recruit agents who do not fit the profile. Bin Laden himself, in his handwritten journals, “exhorted followers to explore ways to recruit non-Muslims…—particularly African Americans and Latinos” (New York Times, May 12, 2011).

This article contributes to this debate by providing theoretical analysis and experimental validation to guide policy makers to improve the effectiveness of targeted and/or profiled screening. Our research investigates the conditions under which profiling is a rational and efficient counterterrorism policy. Although our work is related to the previous economic literature, we take a somewhat different approach by assuming that the terrorist group rationally chooses individuals with certain characteristics to carry out its attacks, rather than viewing terrorism as the result of decentralized individual choices. In the model, the terrorist group (attacker) decides which demographic “type” to send through a security checkpoint. The security officials (defender) decide which type or category to subject to an extensive search. Some types (for instance, young males with military and ideological training) are more “reliable” than others (women and children) in the sense of having a higher probability of mounting a successful attack once they pass undetected through a security checkpoint. If the attackers were not selective, sending a mix of types with equal probabilities, then defenders would use limited resources to search the most reliable types who would cause the greatest damage if they passed security. Consequently, attackers would respond by sending less reliable types more often. In turn, defenders would respond by defending less reliable types more often. In equilibrium, attackers and defenders should not have any additional incentive to change their strategies. We show that, in a mixed strategy Nash equilibrium, there is a tendency to use low-reliability attack strategies and high-reliability defense strategies. Thus, attack and defense strategic patterns are seemingly “misaligned,” even though both players are rational and there are no surprises in terms of observed behavior.

Our profiling game is similar in spirit to a two-person “hide-and-seek” game in which the hider decides where to place an object and the seeker decides which of n locations to search. The hider wins if the locations do not match, and the standard zero-sum version of this game has (hider, seeker) payoffs of (1, 0) if the location decisions do not match and (0, 1) otherwise.² Our profiling game is similar in that the defender desires to match by searching the demographic type selected by the attacker, who in turn desires to select a type that does not match. However, our profiling game is different in that the different demographic “types” are assumed to have different success or “reliability” probabilities, an asymmetry that introduces asymmetries in the attack and defense probabilities across attacker reliability types. As a result, in some cases, only a subset of reliability categories are actually used in equilibrium, and within this subset the defense probabilities and the terrorists’ attack probabilities are inversely related, with the government searching less reliable types less frequently and the terrorists sending them more frequently.

With only two locations, hide-and-seek games are sometimes referred to as “matching pennies” games, and such games have been used to analyze strategic play in professional sports contests, for example, whether to pass or lob in tennis or to which side of the goal to direct a penalty kick or defense (Chiappori, Levitt, and Groseclose 2002). Matching pennies games have also been used to model predator–prey interactions, where the predator desires the match. These games are structured to be realistic for the biological applications considered, and payoffs can be stochastic. For example, the Avrahami, Güth, and Kareev (2005) “parasite game” is a hide-and-seek game preceded by a move by “nature” that randomly determines which of two locations will have a food resource. The “producer” selects a location to look for food and harvests if it is present. The “parasite” then selects a location to search, in order to steal the food if it has been harvested by the producer. Our profiling model also has stochastic payoffs, but the focus is on a monotonic array of reliability parameters for a set of possible attacker types and on the monotonic arrays of attack and defense probabilities that can extend to n-categories or types.

We use an experiment to assess the extent to which individual decisions are consistent with theoretical predictions of misaligned profiling. The experiments are motivated, in part, by the somewhat counterintuitive nature of equilibrium patterns of the randomized strategies. In particular, the theory produces a paradox of misaligned profiling: in equilibrium, the high-reliability categories are searched more intensively, even though they are used less intensively by the terrorist organization. Field experiments with “professional” terrorists and security officials to test these predictions would be expensive and controversial, if possible at all, and the results would surely be confidential. Instead, we rely on laboratory experiments, which provide the ability to replicate and control the environment, even though the laboratory environment is admittedly highly simplified. The results of the experiment reveal behavioral patterns that are consistent with predicted patterns. However, we also find several interesting behavioral deviations, with defenders tending to search more reliable attacker types more often than predicted.

Theoretical Model and Predictions

To address the problem of profiling, consider a simple two-player model of screening at security checkpoints. The first player represents a government agency that is attempting to discover terrorists, for example, military officers at a checkpoint, Transportation Security Agency officials at an airport security counter, or other agencies dealing with homeland defense, such as the Coast Guard, the Border Patrol, the Customs Service, or the Immigration and Custom Enforcement department of the Department of Homeland Security (DHS). Their objective is to identify any terrorists attempting to penetrate their checkpoint and, thereby, block an attack. The second player represents a terrorist group, which is assumed to be centrally directed, strategically rational, and motivated by a desire to penetrate the defenses and commit an attack. Experts agree that there is usually a strategy behind terrorists’ actions. Whatever form it takes, terrorism is typically not random or blind; it is a deliberate use of violence against civilians for political or religious reasons. Therefore, following the spirit of most game theoretic literature on terrorism, we model terrorists as rational actors; for an excellent survey, see Sandler and Arce (2007).³ In what follows, we refer interchangeably to the terrorist as the “attacker” and to the government agency as the “defender.”

The main motivation for our research can be illustrated with a simple model taken from Kydd (2011). The population of individuals passing through the checkpoint is divided into n ≥ 2 different observed categories or types. A successful attack by a person from any category will result in a gain of G for the terrorist and a loss of L for the government security agency. Let the n categories be indexed by i, where the lower the value of i, the higher the chances an undetected person would succeed in carrying out the attack. The probability that a person from category i will succeed if undetected is denoted by r_i , with r ₁ > r ₂ > r ₃ >…> r_n . We will refer to r_i as the “reliability” of category i. Each category could be identified and determined by different criteria, such as age, gender, and country or region of origin, religion, or any other observable personal characteristic. For instance, the New York Times on June 27, 2011, reported that in a remote area in central Afghanistan “insurgents tricked an 8-year-old girl…into carrying a bomb wrapped in cloth that they detonated remotely when she was close to the police vehicle.” This is an example of an attack using a person from a less reliable type or category who is less likely to be searched.⁴

We assume that the defender selects one category to search and that the search is fully effective in detecting the attacker.⁵ Hence, the attacker of type i who is searched would fail, and one who is not searched would carry out an attack with probability of success r_i . Let d_i denote the probability of defending against type i, and let a_i denote the probability of attacking with type i, with 0 < d_i , a_i ≤ 1. Then, a person from category i would succeed only if the defender searches another type and the attack turns out to be successful, an outcome that occurs with probability (1 − d_i )r_i . The attacker, therefore, faces a trade-off between sending high-reliability people and sending others who are less likely to be searched. If the attacker uses type i with probability a_i , then the defender’s probability of a loss from defending against type i is (1 − a_i ) times the average reliability across all other types.

Before deriving the equilibrium, it is useful to provide some intuition. The equilibrium involves randomization, since a deterministic attack via one type would lead to a sure defense there, and a deterministic defense against one type would lead to a sure attack via another. In equilibrium with randomization, the expected payoffs for all decisions used must be equal, otherwise the player would prefer decisions with higher expected payoffs. The main result reveals a paradox of misaligned profiling: in equilibrium, the high-reliability types are searched more intensively, even though they are used less intensively by the terrorist organization. This is a paradox in the sense that the equilibrium pattern makes the defense strategy appear to be misguided, and hence, ineffective, which is not the case. Second, there will be a cutoff point beyond which the defender will not bother searching at all, so types with a low reliability score will be ignored and not searched. Third, the attack probabilities will actually increase as the category’s reliability declines, up to a cutoff point, after which the probabilities will decline to zero. That is, a set of low reliability categories will not be recruited by the attacker nor searched by the defender. Within the set of higher reliability categories, the defense probabilities and the terrorists’ attack probabilities will be inversely related, with the government searching less reliable categories less frequently and the terrorists sending them more frequently.

The key structural feature of our model is the difference in attack success reliabilities for different attacker types. The increasing probabilities of success of increasingly reliable attacker types introduce a stochastic element into the payoff functions, which differentiates our model from standard hide-and-seek games in which the person doing the hiding will win with probability 1 if the seeker looks elsewhere. In our model, the monotonic ranking of attacker-type reliabilities generates misaligned, monotonic attack and defense profiles, with defense probabilities increasing in attacker-type reliability, and with attack probabilities inversely related to reliability, at least for the range of attacker types that are actually used with positive probability in equilibrium. The n-dimensional nature of the attack and defense decisions also differentiates our model from other games with stochastic payoff elements, such as penalty kicks games in soccer where the kick can go to one side or the other, or a two-player food search game with two locations.⁶ In particular, the attack and defense probability predictions for the n-dimensional profiling model we consider are shown to be monotonic in the ranked reliability parameters and to be inversely related or misaligned.

The intuition behind misaligned profiling is surprisingly simple. An attacker choosing between n different reliability types would have an expected payoff of G(1 − d_i )r_i from selecting type i. It must be the case that these attacker-expected payoffs are equal for all types that are used with positive probability in equilibrium; that is, G(1 − d_i )r_i = π _a , where π _a is the attacker payoff in equilibrium. Since the right side of the equation is a constant with respect to i, the inverse relationship between d_i and r_i on the left makes it clear that the attacker types with higher reliability are defended with higher probabilities. An analogous argument can be constructed from equating defender expected payoffs and removing terms in sums that cancel out, to show that attack success probabilities are equalized: a_ir_i = a_jr_j for all types of i, j used with positive probability, and hence, attack probabilities and associated type reliabilities are inversely related in equilibrium.

These results can be illustrated for the special case of a two-category zero-sum game, in which a successful attack results in payoffs of 1 for the attacker and −1 for the defender. To be willing to randomize, the attacker’s expected payoff for sending either type must be equal, that is, the product of the probabilities of not being searched and of succeeding are the same for both categories: (1 − d ₁)r ₁ = (1 − d ₂)r ₂. Since 1 − d ₂ = d ₁, we obtain a single equation, (1 − d ₁)r ₁ = d ₁ r ₂, which can be solved for defense probability against type 1:

D e f e n s e p r o b a b i l i t y a g a i n s t t y p e 1 : d_{1} = r_{1} / (r_{1} + r_{2}) .

Since type 1 is more reliable, r ₁ > r ₂, it follows that d ₁ > d ₂, or the defender searches the more reliable type 1 more often, which is intuitive.⁷ Conversely, for any given attack probabilities a ₁ and a ₂, a defense against type 1 will result in a loss with probability a ₂ r ₂, whereas a defense against type 2 will result in a loss with probability a ₁ r ₁. Since a ₂ = 1 − a ₁, the equality of expected defender payoffs results in an equation, (1 − a ₁)r ₂ = a ₁ r ₁, which can be solved for the attack probability via type 1:

A t t a c k p r o b a b i l i t y v i a t y p e 1 : a_{1} = r_{2} / (r_{1} + r_{2}) .

Hence, the counterintuitive result that a ₁ < a ₂; that is, in equilibrium, the attacker uses the more reliable type 1 less often, since r ₂ < r ₁.^8,9

Experimental Design and Procedures

Our objective is to evaluate the extent to which observed behavior is consistent with theoretical predictions. To this end, we design two treatments with (r ₁ = .67, r ₂ = .33) and (r ₁ = .80, r ₂ = .20). For simplicity, we selected reliability parameters that sum to 1 in both treatments: r ₁ + r ₂ = 1. In the 67/33 treatment, type 1 is twice as reliable as type 2. Theoretical prediction is that the defender searches type 1 with probability d ₁ = 2/3 and the attacker uses type 1 with probability a ₁ = 1/3. Conversely, the probability of defense against type 2 is d ₂ = 1/3 and the probability of attack via type 2 is a ₂ = 2/3. The best-response functions for this game are shown in Figure 1.¹⁰ For example, if the probability of an attack via type 1 is low (left-hand side), the probability of a defense against type 1 is low (bottom left part of the figure). Conversely, if the probability of defense against type 1 is high (top), then the attacker will use type 1 with probability 0 (upper-left-hand side). The intersection of the best response lines determines the equilibrium, with a 2/3 probability of a defense against type 1, and a 1/3 probability of an attack via type 1.

Figure 1.

Best responses and equilibrium in the 67/33 treatment.

In the 80/20 treatment, we increase the reliability of type 1 so that type 1 is four times more reliable than type 2; that is, r ₁ = .80 and r ₂ = .20. The prediction of the theory is that since type 1 is more reliable, the probability of defense against type 1 should increase to d ₁ = 4/5, while the probability of attack via type 1 should decrease to a ₁ = 1/5. Correspondingly, the probability of defense against type 2 should decrease to d ₂ = 1/5, while the probability of attack via type 2 should increase to a ₂ = 4/5.

Subjects for the experiment were recruited from student populations at the University of Virginia, with the promise that they will “participate in a research experiment” and will receive a fixed payment of US$6 plus additional cash earnings, which will depend on their own and others’ decisions. When subjects arrived in the lab, they were seated in visually separated cubicles with networked computers. The software kept track of total earnings, and subjects were paid in cash at the end of each session, after they signed receipt forms. A total of 144 subjects participated in the experiment with 72 subjects (thirty-six pairs) participating in one treatment and 72 subjects (thirty-six pairs) participating in the other treatment. Instructions for the experiment are included in the online Appendix. The screen displays listed the most reliable category on the left-hand side for half of the subject pairs and on the right side for the other half. The experiment was run in a series of sessions consisting of twelve to eighteen subjects each, with fixed pair matching for fifty rounds. Subjects in each pair were given the role of attacker or defender and stayed in that role in all rounds of the experiment.

In each round, the attacker chose a category corresponding to a type of terrorist agent (type 1 or type 2), and the defender chose a profiling strategy, or type of person to search. If the selected categories matched, then the attack failed. If the selected categories did not match, then the attack success probability was determined by the reliability of the attacker’s category choice. A successful attack resulted in a fixed payoff of 1 dollar to the attacker and a loss of US$1 for the defender. The payoffs were added to private incomes of US$1 for the defender and US$0.60 for the attacker in each round. These outside incomes were selected to equalize final payoffs and were private information (defenders did not know attacker incomes, and vice versa). On average, subjects earned US$26, and the experiment lasted for about thirty minutes.¹¹

Results

Table 1 reports for the two treatments the predicted and average observed probabilities of defense and attack for type 1, respectively, from the first round, the second half and all fifty rounds of play.

Table 1.

Experimental Data and Predictions.

	Treatment
	67/33		80/20
	d₁	a₁	d₁	a₁
Predicted probabilities	0.67	0.33	0.80	0.20
First round average data	0.81	0.36	0.92	0.19
Second half average data	0.78	0.30	0.88	0.20
All rounds average data	0.79	0.31	0.88	0.22

We begin by analyzing the data from the 67/33 treatment. Figure 2 displays the average defense and attack probabilities, while Figure 3 displays the average attack and defense probabilities for each of the thirty-six fixed pairs. As predicted by the theory, there is strong “misaligned profiling.” Specifically, the defenders search more reliable type 1 with higher probability than less reliable type 2 (0.79 vs. 0.21; Wilcoxon signed-rank test, p value < .01, n = 36).¹² Conversely, the attackers employ more reliable type 1 with lower probability than less reliable type 2 (0.31 vs. 0.69; Wilcoxon signed-rank test, p value < .01, n = 36).

Figure 2.

Average data for all rounds and theoretical predictions in the 67/33 treatment.

Figure 3.

Attack and defense probabilities for 36 fixed pairs in the 67/33 treatment.

Relative to theoretical point predictions, we find that defenders tend to defend against the more reliable type 1 more than predicted (0.79 vs. 0.67; Wilcoxon signed-rank test, p value < .01, n = 36). The behavior of attackers is not significantly different from theoretical predictions for category 1 (0.31 vs. 0.33; Wilcoxon signed-rank test, p value = 0.42, n = 36).

One may argue that subjects in a role of defender search type 1 more often because this option is presented to the left from type 2. In a related literature on multibattle contests, called Colonel Blotto games, where attackers and defenders allocate resources on multiple battlefields, it is documented that subjects often exhibit allocation bias toward left battlefields (Chowdhury, Kovenock, and Sheremeta 2013).¹³ Nevertheless, it is unlikely that allocation bias can explain our data, since in half of the sessions type 1 option was presented to the left from type 2 and in the other half it was presented to the right. Moreover, the probability that the defender searches type 1 is virtually the same disregarding whether type 1 is located to the left or to the right of type 2 (0.79 vs. 0.79; Wilcoxon rank-sum test, p value = 0.72, n ₁ = n ₂ = 18).

The pattern of data that we observe in the 67/33 treatment is also observed in the 80/20 treatment with r ₁ = .80 and r ₂ = .20. Figures 4 and 5, displaying the average defense and attack probabilities for the 80/20 treatment, show even stronger “misaligned profiling.” Specifically, the defenders search more reliable type 1 with much higher probability than less reliable type 2 (0.88 vs. 0.12; Wilcoxon signed-rank test, p value < .01, n = 36). Conversely, the attackers use more reliable type 1 with much lower probability than less reliable type 2 (0.22 vs. 0.78; Wilcoxon signed-rank test, p value < .01, n = 36). As before, the defenders tend to defend against the more reliable attacker type 1 more than predicted (0.88 vs. 0.80; Wilcoxon signed-rank test, p value < .01, n = 36). This behavior cannot be explained by the allocation bias, since the probability that the defender searches type 1 is very similar in sessions where type 1 is located to the left versus sessions where type 1 is located to the right of type 2 (0.86 vs. 0.90; Wilcoxon rank-sum test, p value = .19, n ₁ = n ₂ = 18).

Figure 4.

Average data for all rounds and theoretical predictions in the 80/20 treatment.

Figure 5.

Attack and defense probabilities for 36 fixed pairs in the 80/20 treatment.

A comparative static prediction of the theory is that increasing reliability of type 1 should increase the defense probability against this type. This is exactly what we observe in the experiment. When the reliability of type 1 increased from r ₁ = .67 to r ₁ = .80, the defense probability against type 1 increased from .79 to .88 (Wilcoxon rank-sum test, p value < .01, n ₁ = n ₂ = 36). The prediction for the attacker is the opposite, increasing reliability of type 1 should decrease the probability of using type 1. Again, we observe this in the experiment. When the reliability of type 1 increased from r ₁ = .67 to r ₁ = .80, the probability of using type 1 by the attacker decreased from 0.31 to 0.22 (Wilcoxon rank-sum test, p value = .01, n ₁ = n ₂ = 36).

Although the data averages are close to Nash predictions for the two treatments, there is a clear tendency for defenders to defend against the more reliable type more often than predicted (the attackers’ behavior, on the other hand, is quite close to the Nash predictions). These deviations from Nash predictions are not large in magnitude, but it is notable how the deviations are largely concentrated among defenders in both treatments. These deviations are in an intuitive direction for defenders, who might find it natural to overdefend against high-reliability attack types, whereas the Nash prediction for attackers is less intuitive, that is, attack more often with the less reliable attacker type.¹⁴ Even if this strategy is less intuitive, it does show up in the very first round of play, where it seems that attackers expect that defenses are more likely to be targeted to more reliable attack types. One way to model such strategic thinking about what the other person might do is to use a “level-k” analysis (Stahl and Wilson 1994, 1995).¹⁵ After the initial round of play in the experiment, however, a level-k analysis is less appropriate since subjects probably learn more from their own experience than from introspection and levels of strategic thinking. Moreover, a level-k analysis of best responses to level k − 1 is the same for both of our treatments, so this approach cannot explain the salient treatment effect in the data, an effect that is predicted by the Nash equilibrium.

Another approach that we considered is the quantal response equilibrium (QRE) introduced by McKelvey and Palfrey (1995), which in this case adds curvature to the sharp-line best response function in Figures 1 and 2 and would tend to pull attack probabilities closer to .5. Such a smoothing, however, could not explain the observation that attack probabilities are close to Nash predictions, while the probability of defense of the high-reliability type is even more extreme than predicted. It is worth noting that the QRE has been useful in explaining “own-payoff effects” in 2 × 2 matrix games (McKelvey and Palfrey 1995; Goeree and Holt 2001; Goeree, Holt, and Palfrey 2003, 2005) with asymmetries that differ from those that arise in our profiling model.¹⁶ One asymmetry in the profiling game used in our experiment is that an attacker may feel some extra regret when a low-reliability attack type is used and is not defended against, but fails anyway. Several subjects mentioned this type of reaction in an informal debriefing conversation after one of the sessions. Another possible approach to explaining deviations from Nash predictions could involve probability weighting, for example, a tendency to overweight the relatively low probability (.33 in equilibrium) of an attack with a reliable type may cause the defender to overdefend against that type.¹⁷ While some of these approaches seem plausible, we believe that any ex post explanation would be tenuous at best without additional research.

Conclusion

This article implements an experimental test of a game-theoretic model of equilibrium profiling. Attackers choose a demographic “type” from which to recruit, and defenders choose which demographic types to search. Some types are more reliable than others in the sense of having a higher probability of carrying out a successful attack if they get past the security checkpoint. Using a controlled laboratory experiment with financially motivated human subjects, we find strong support for game-theoretic model of equilibrium profiling. Consistent with theoretical predictions, the defenders search more reliable types with higher probability, while the attackers employ more reliable types with lower probability than less reliable types. However, we also find small (but systematic) deviations with defenders searching more reliable types more often than predicted. These deviations, however, do not obscure the clear pattern of misaligned profiling and the sharply different effects of attacker-type reliability parameters on predicted and observed attack and defense propensities.

There are several important implications of our findings. The DHS in October 2010 issued the following statement: “As a precaution, DHS has taken a number of steps to enhance security.… Passengers should continue to expect an unpredictable mix of security layers that include explosives trace detection, advanced imaging technology, canine teams and pat downs, among others.” As our theoretical model predicts and experimental results confirm, a security agency such as the DHS or the Transportation Security Agency must respond optimally to terrorist organizations’ actions and preempt any terrorist attack by identifying terrorists within large groups of mostly innocent people. In this context, profiling is rational and the government should actually screen individuals according to their potential to be reliable recruits for the terroristic organization. The security agency should search more often the individuals belonging to the most reliable categories with an apparently unfair profiling practice. The intense search directed toward high-reliability individuals should induce the terrorists to send less reliable categories more often. Our findings should be interpreted with caution, however, since our experiment does not shed light on the indirect effects of profiling, for example, the possible increases in a propensity for terrorist activity among groups being profiled (Harcourt 2007).

There are many possible avenues for future research. The general n-type version of the model presented in the Theoretical Model and Predictions section also predicts misaligned profiling for the types that are reliable enough (sufficiently high r_i values) to be used in equilibrium, with a minimum reliability cutoff that separates types that are used from those that are not. These predictions with n possible attacker types could be compared with data. In particular, it would be interesting to see whether high-reliability attack types are overdefended relative to the theoretical predictions in this richer setting, as observed in the simple model with only two attacker types. In addition, it would be interesting to investigate both theoretically and experimentally a nonconstant sum version of the profiling game, where each player can choose to attack (or defend) more categories at once and the cost of attacking (or defending) is increasing in the number of categories attacked (or defended). Another avenue would be to introduce multiple attackers and defenders, with defenders trying to defend against multiple independent (or dependent) attackers. Also, it is important to examine the problem of profiling in the setting of incomplete information, that is, when defenders and attackers know only the distribution of the reliability of each type. In such case, players would need time and experience to learn how reliable different types are. These are all very interesting questions, and we leave them for future research.

Footnotes

Acknowledgment

We thank two anonymous referees and the Editor of this journal for their valuable suggestions. We have benefitted from the helpful comments of Rachel Croson, Catherine Eckel, seminar participants at the University of Virginia, the University of Texas at Dallas, SUNY-Buffalo and participants at the North American Economic Science Association Conference in Tucson. We also wish to thank Michael Patashnik and Emily Snow for research assistance.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Research support provided by the University of Texas at Dallas, the Virginia Commonwealth Presidential Research Incentive Program and NSF grant NSF/NSCC-0904695 to Razzolini is gratefully acknowledged. Holt’s work on the project was funded in part by NSF/NSCC grants 0904795 and 0904798 and BCS-0905044, and the UCS CREATE National Center for Risk and Economic Analysis of Terrorism Events.

Notes

Supplemental Material

The online [appendices/data supplements/etc] are available at .

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