To Pay or Not to Pay: Criminal Extortion from a Game Theory Perspective

By: MAJ Michael E. Loconsolo, U.S. Army

The Dilemma: Over the past decade, the Mexican government has spent prodigious resources attempting to halt the increasing power and influence of drug cartels throughout the country. An offshoot of the growing power of cartels is their ability to threaten businesses through the illegal enterprise of extortion. Mexican authorities have seen an exponential increase in reported threats and extortion rackets throughout the country.1 As a result, local business owners face a deadly dilemma: if cartels seek to extort their business, should owners cooperate by overlooking illegal activity and paying extortion fees? Or should business owners stand up to the cartels by refusing to pay extortion fees and notifying the authorities of the cartels' illegal activity? Through the use of game theory under current security conditions, this article shows that business owners achieve their best outcome by organizing a fierce, unified resistance against the cartel's efforts to extort. This united resistance ultimately allows local business owners and the cartel that is threatening them to reach an agreement whereby the cartel promises not to pursue extortion while the business owners promise to turn a blind eye to drug trafficking and other illegal activities. In the absence of effective law enforcement, the resulting decrease in local violence and economic damage from such a "truce" can be seen as the community's best outcome as well.

The Game

Figure 1 depicts the extortion dilemma using ordinal rankings (where "4" is best and "1" is worst) with two players, a business owner and the cartel:


A business owner is willing to pay "protection" fees and turn a blind eye to illegal cartel activities.

Cartel: This is the best scenario for the cartel, because it receives revenue without any resistance from the business owner and without fear of police interference.

Business owner: This is the third best (i.e., next to worst) scenario for the business owner. Although he is willing to pay fees and turn a blind eye to illegal cartel activities in exchange for relief from violence, he surrenders his profits and ultimately resides in a threat- and crime-filled environment.


The cartel attempts to extort a local business owner but meets staunch resistance: the business owner refuses to pay extortion money and notifies the authorities.

Cartel: This is the second best scenario for the cartel. Although the cartel has to use threats and violence against the business owner, in the absence of effective police action it still gets its money.

Business owner: This is the worst scenario for the business owner, because in much of Mexico, the local authorities typically cannot match the power and influence of the cartels. As a result, the cartel is still able to extort the business owner, but does so through violence and punishment.


The business owner is willing to pay fees and turn a blind eye to cartel activities, but the local cartel does not have any interest in extortion.

Cartel: This is the third best scenario for the cartel. On the one hand, it willingly chooses to forgo a significant source of income from extortion; on the other hand, it still has the freedom to conduct other illegal activities without the risk of locals notifying the authorities.

Business owner: This is the second best scenario for the business owner, because he is able to maximize his profit without the need to pay the cartel for "protection." By turning a blind eye to other crime, however, he has to operate his businesses in a crime-ridden environment that affects overall sales.


The business owner vows to resist the cartel's presence in his town and works with the authorities to stop the cartel's illegal activities, even though the cartel does not try to extort money from any of the local business owners.

Cartel: This is the worst scenario for the cartel. It chooses not to extort money but the business owner is not content with the cartel's other illegal activities in the town and assists authorities in identifying and arresting cartel members.

Business owner: This is the best scenario for the business owner and the town because everyone can run their respective businesses without the threat of criminal extortion. They also assist authorities in weeding out crime, thereby attracting greater business from outside areas.

Nash Equilibrium

Figure 2 identifies a Nash equilibrium2 at the point (AC)—the cartel extorts the business owner, who decides to pay fees and turn a blind eye to illegal cartel activity. In addition, the illustration shows that the cartel has a dominant strategy to extort the local business owner regardless of the business owner's decision to cooperate or resist. Although no reasonable business owner would like to pay extortion fees, the threat of violent consequences from resisting is less desirable than simply appeasing the cartel by paying the fees and turning a blind eye to illegal activity.

Strategic Moves

This section examines strategic moves by the cartel as well as the business owner. It considers potential consequences associated with each decision.

First Move

Business owner: If the business owner decides to make the first move, he determines that since the cartel has a dominant strategy of extorting money, the best outcome that the business owner can secure is the third best scenario at (AC): pay extortion fees and turn a blind eye to illegal cartel activities.

Cartel: If the cartel decides to make the first move, it determines that by choosing to extort money, the local business owner will prefer to pay and turn a blind eye rather than resist the cartel and risk violence. By making the first move, the cartel can secure its best scenario at (AC): charge extortion fees from a cooperative business owner.

Regardless of who makes the first move, it is reasonable to assume that under these conditions, the cartel will seek to extort money while the local business owner complies and turns a blind eye to the cartel's illegal activities.


Business owner: The business owner can threaten to resist the cartel and notify authorities if the cartel pursues extortion. His intent is to persuade the cartel to cease extortion efforts against his business. Under the conditions of this game, the cartel still prefers to extort money from the business owner, even if he resists. As we pointed out earlier, this is the worst scenario for the business owner, because his counter-threat does not work and the cartel takes his money through violence.

Cartel: With a dominant strategy of extortion already in place, the cartel does not have a further threat.


Business owner: Similar to a threat, the business owner also has a promise to offer. In this scenario, the business owner can promise to turn a blind eye to illegal cartel activity as long as the cartel agrees to avoid any extortion of his business. Under the current conditions of this game, the cartel achieves a better outcome by extorting the business anyway. As a result, even though the business owner agrees to turn a blind eye, the cartel continues to extort money from him. The promise does not work.

Cartel: Under the game's current conditions, the cartel can promise the business owner that it will not extort money if he turns a blind eye to illegal activities. While this is a reasonable promise, it is still worse than the likely first move. As a result, the cartel is better off without offering any promise to the business owner.


Business owner: A combination of threat and promise is a potential point of negotiation for the business owner. In a combination strategic move, the business owner can threaten to resist and notify authorities if the cartel seeks extortion, but promise to turn a blind eye to illegal operations if the cartel avoids extortion activities. Under the pure conditions of the game as I've labeled them, the cartel would reject this offer and prefer extortion. The following section explores scenarios in which such an offer might be acceptable to the cartel.

Cartel: The cartel does not have a combination strategy.

Security Levels/Prudential Strategy

Security Levels

Figures 3 and 4, respectively, identify each player's security level. In a twoplayer game, a player's security level is his maximum gain after his options have been minimized by the other player's actions. Consider, for example, the business owner's preferences. Using the preferences listed in figure 3, the business owner can achieve a 2 or a 3 if he decides to turn a blind eye to the cartel's crimes. Knowing this, the cartel minimizes the business owner's security through the use of extortion (2 < 3). Conversely, the business owner can achieve either a 1 or a 4 if he decides to resist payments and notify the authorities. Knowing this as well, the cartel again minimizes the business owner's security through extortion (1 < 4). The cartel's commitment to extortion effectively minimizes the business owner's well-being, and restricts the maximum gain the business owner can achieve. Knowing this, the business owner prefers to turn a blind eye (settling for a 2) rather than resist payment (resulting in a 1). Thus, the business owner's security level is 2.

Figures 3 and 4 identify each player's security level by maximizing each player's own gain while minimizing the gain of the other player.

Business Owner's Security Level: The business owner's security level is 2 (see figure 3). This means that in the worst case, the business owner can guarantee what he considers to be the third best scenario: the cartel pursues extortion, and the local business owner agrees to pay fees and turn a blind eye to illegal activity.

Cartel's Security Level: The cartel's security level is 3 (figure 4). This means that in the worst case, the cartel can guarantee what it considers to be its second best scenario: although the business owner resists, the cartel uses threats and violence to pursue extortion.

Prudential Strategy

Figure 5 illustrates that using both security levels, the status quo is found at (2,3), a situation much more favorable to the cartel than to the business owner. The status quo describes the existing state of affairs in a disturbingly large number of towns throughout Mexico. The Washington Post recently noted that in 2012, reports of extortion doubled in Mexico while most other types of crimes declined.3 In addition, authorities suspect that a significant number of additional extortions occurred that simply were not reported to local police, probably for fear of reprisal.4 Nash's game theory provides an accurate reflection of this unfortunate state of affairs.

Both solutions are found in pure strategies, suggesting that in order to meet its guaranteed minimal payoff, the cartel should always pursue extortion, while the business owner will suffer the least by cooperating with the cartel, paying extortion fees, and turning a blind eye to the cartel's other illegal activities.

How to Resolve the Extortion Dilemma

Presumably, there is no rational business owner who prefers to pay extortion fees. I make the assumption that rational business owners, whether actively or passively, will search for a solution to eliminate extortion payments. This section considers several actions that might alter the preferences of either the business owner or the cartel, and how those changes ultimately affect each side's strategy. It suggests a strategy where the business owner is better off than Mexico's current status quo.

Increased Security Presence

Most logically, the business owner would benefit from a more robust and effective police force that has the strength to overwhelm and defeat the cartel. In this scenario, the effectiveness of the police force serves as a deterrent to extortion practices. The cartel's preference shifts as a result: now the cartel's second best preference is not to extort if the business owner turns a blind eye to illegal activities (AC). Conversely, the cartel's option to extort money from the business owner who will resist and notify authorities (BC) becomes its third best preference. All other preferences remain the same.

Figure 6 illustrates the new preferences and corresponding Nash equilibrium.

Without communication between the business owner and the cartel, however, nothing changes for the business owner. The cartel still has a dominant strategy in pursuing extortion. Consequently, the Nash equilibrium remains where the cartel extorts while the business owner pays and turns a blind eye to illegal activity. What has changed is the business owner's leverage in strategic moves. If effective police operations increase a business owner's leverage, the business owner can offer the combination of a credible threat and promise to improve his outcome.

Solution: Should the cartel pursue extortion, the business owner can threaten to resist and notify the authorities (eliminating AC). This threat does not work alone, however. Game theory suggests that the business owner would also have to promise to turn a blind eye to the cartel's illegal activity (eliminating BD). By combining the threat and promise, the business owner can secure an agreement: the cartel will not extort in exchange for the business owner's blind eye to other illegal activity (AD).

Community Organization against Crime

In an ideal world, the Mexican police forces would maintain the trust of the people and wield the strength to defeat the drug cartels that are terrorizing an increasing number of businesses and communities throughout Mexico. Unfortunately, the reality is that widespread corruption within the police forces leads many business owners to question police motives and to hesitate to call on them for help. Furthermore, the drug cartels have grown so strong that in some areas of Mexico, they frequently outgun and outmatch the government forces that are tasked to protect the population.5 In some instances, Mexican business owners have grown tired of the status quo and have sought ways to mount a collaborative effort among themselves against cartel activity.

Figure 7 illustrates the preferences and corresponding Nash equilibrium if business owners collectively decide to resist the cartel rather than cooperate individually with extortion and other criminal activities.

In this scenario, the game changes in that the single business owner is replaced by a collective group of business owners with a common preference. It is apparent that a simple shift in the business owners' preference to resist and notify authorities has little effect on the cartel's actions. The cartel maintains a dominant strategy to extort businesses through any means necessary, and the resultant Nash equilibrium shifts to BC: extortion against a resistant community. This scenario is likely to result in the most chaotic, violent environment of any of the preferences. Furthermore, the business owners pin themselves in a corner where neither threat nor promise will persuade the cartel to change its activities. So, how can business owners create an incentive where resistance to cartel activity might cause the cartel to change its strategy and eliminate extortion?

One suggestion is that any organized resistance must be conducted with total commitment against the cartel. As mentioned previously, a simple shift in the business owners' preference to resist is not enough to eliminate extortion. Business owners must form a resistance so unified and fierce that it shifts the preference of the cartel as well. Specifically, the cartel would prefer to simply conduct its illegal activities without extortion in exchange for a blind eye from the business owners (AD) rather than trying to extort a fiercely resistant community (BC). Figure 8 illustrates the new preferences and corresponding Nash equilibrium.

Solution: While the Nash equilibrium remains at BC, strategic moves now suggest that both sides have a promise that would make the outcome more preferable for both parties. The business owners promise to turn a blind eye if the cartel does not extort their businesses. Similarly, the cartel promises to cease extortion if the business owners agree to turn a blind eye to the cartel's other illegal activities. In this classic prisoners' dilemma, game theory suggests that the resultant outcome would be at AD, the second best outcome for both parties. Unless police and military forces can make strong gains against cartel activity, it is arguably in the best interest of Mexican business owners to work together to take resistance efforts into their own hands (figure 9).

Case Study: Ayutla, Guerrero, Mexico

The past few years have seen an increase in the formation of various vigilante groups throughout Mexico that are focused on resisting the violent drug cartels. One news source recently reported that in the southern Mexican state of Guerrero, "a vigilante movement [was] born of frustration at extortion, killings, and kidnappings that local police are unable, or unwilling, to stop."6 No one, from the store owner to the bus driver, seemed to be exempt from the protection payments demanded by cartel members. Initially, business owners preferred to cooperate with the cartel and resorted to raising the prices of their products and services to make up their losses. "When they extorted money from the rancher, he raised the price of beef, and the store owner raised the price of tortillas," explained a local vigilante in the town of Ayulta.7

The rise in intimidation and extortion by the cartel ultimately pushed the citizens of Ayulta to their limits; in January 2013, the town created the Las Mesas vigilantes. The business owners reached the point where they preferred to resist rather than passively comply with cartel demands. According to the Las Mesas commander, drug activity is frowned upon by locals but is not the target of this upstart resistance movement. "We are not against those who are distributing drugs. That's a way for them to earn a living. …What we are against is them messing with the local people," explained the group's commander.8 The result has been growing support, both active and passive, from the local population for increased resistance against unpopular cartel intimidation. One local resident explained, "In less than a month, [the vigilantes] have done something that the army and … police haven't been able to do in years."9 One might suggest that in line with the game theory model, the cartel is beginning to shift its preference: it now prefers to stop extortion in return for the community's blind eye to drug activity, rather than try to continue extortion efforts against an armed, strongly resistant community.


Mexico continues to have a significant problem with powerful, violent, and influential drug cartels. Although cartels do not plague the entire country, many areas are severely affected. While security forces continue the fight, internal corruption and lack of resources have made it difficult for them to garner the trust and support they need from affected populations in local communities. As extortion efforts have increased, local business owners have helplessly obliged the cartels' demands and suffered the economic consequences. Growing discontentment with the status quo has led to an increase of popular resistance against cartels across Mexico. Business owners are increasingly exasperated with the security situation and have decided to collaborate in efforts to eliminate the cartels' impact on their local communities.

While most business owners would prefer to turn the responsibility for security over to a trustworthy police force with the capability to eliminate extortion and other cartel activity, few perceive this as a serious option for the near future. Instead, business owners need strong resolve to shift their preference and resist extortion rather than accept it as an inevitable way of life. Resistance must be strong enough to shift the cartel's preference as well. Once the cartel sees greater benefit in coexisting with the locals without disrupting their businesses, a mutual agreement can be reached. As the Ayulta defense commander suggested, business owners can promise to turn a blind eye to drug trafficking in exchange for an end to extortion and intimidation. Despite continuing drug activity, the new status quo would allow businesses to operate without the fear and violence that plagues their society.

For the Mexican government, the cartel problem is a complicated, protracted fight. History suggests that a significant victory against the cartels in Mexico will take years of effective strategy. In the interest of their families, businesses, and overall livelihood, locals can likely benefit most by taking matters into their own hands. While their actions might not solve the problems of drug trafficking, they can defuse cartel violence at the local level and prevent the country from continuing to spiral into extreme chaos.

About the Author(s): MAJ Michael E. Loconsolo is pursuing an MS in Special Operations and Irregular Warfare in the Defense Analysis department, Naval Postgraduate School.


1. "US Chamber Study: Drug Cartels' Extortion Demands on Businesses Make Big Jump in Mexico," Washington Post, 29 May 2013.

2. The Nash equilibrium in game theory is the point at which each of two or more non-cooperative players has made the best choice of strategy he can, knowing the strategies of the other players and knowing that changing his strategy unilaterally will bring no added benefit.

3. "US Chamber Study."

4. Ibid.

5. C. Hawley, "Drug Cartels Outmatch, Outgun Mexico's Police," USA Today, 16 June 2010:

6. "Vigilante Groups Spring Up in Mexico in Fight Against Cartels," Fox News, 21 January 2013:

7. Ibid.

8. Ibid.

9. Ibid.

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