Games of death

     Game theory models used to analyze crime usually assume that there is an external authority that enforces institutions. From example, if the government increases punishment, by setting up the death penalty, a centralized authority will make sure that the death penalty is enforced. In some countries however this is not guaranteed because the government itself is infiltrated by crime and corruption. In this context the institutions that matter are those that emerge from the interaction among individuals. The set of formal institutions is empty. Informal rules are all that matter.

Why do people kill? There are numerous reasons, but lets consider only two reasons: (1) killing for income and (2) killing for power. Other cases are not well defined within these categories.


Examples of killing to gain income are: (a) drug cartels competing for profits, (b) drug cartels killing informants, (c) gangs competing for territory, (d) gangs killing innocents (extortions), (e) thieves killing victims, and (f) political, electoral, killings.

An example of killing to gain power happens when (g) gang members kill innocents as rite of passage.  Less defined cases are: (h) “macho-related” killings, (i) some types of killings of women.

Regarding killings to gain income, we can assume that the purpose of agents is to maximize profits. In the second case, killings to gain power, we can assume that the purpose of the killer is to maximize power.

Giving these assumptions we can set up “games of death” to enlighten our understanding of high crime in countries characterized by a formal institutional vacuum.

(a) Drug cartels competing for profits

A traditional Cournot model used to understand oligopolistic behavior could be used to understand competition among drug cartels. Drug cartels competing for territory, trade routes for example, engage in cartel wars. If a cartel uses a trade route that “belongs” to another cartel retaliation occurs: cartel A will kill members of cartel B, which will foster farther retaliation, cartel B will kill members of cartel A. The process ends up in equilibrium where the reaction functions of both cartels cross each other.  

A relatively stable amount of people will die every period as long as: (1) one cartel interferes with the interests of the other, (2) cartels keep recruiting members, (3) cartels are relatively homogeneous, which rules out the possibility of a take over. If a take over happens the relevant model is that of a monopoly, killings due to cartel wars drop to zero. The monopoly solution also emerges in the case of perfect cooperation among cartels. The Cournot case also applies to case (c), gang competition for territory. In both cases a Nash equilibrium is likely to emerge.

(b) Drug cartels killing informant(s)

In this case the cartel unilaterally, in a dictator’s game way, decides to kill the informant(s). The killing happens as long as informants (journalists for example) venture to express opinions that harm interests of drug cartels. This case also applies to (d) gangs killing innocents, and (e) thieves killing victims, when the victims do not resist. The simplest case of (f) political, electoral, killings lays also in this category, as well as (g) gang members killing innocents as rite of passage.   

(g) “Macho-related” killings

Either because if alcohol or drugs consumption, or because of genetic aggressiveness, etc. One individual challenges another to a fight, the other one accepts or not, and one of them kills the other one (three more solutions are possible).  In contrast with the other cases, this one obeys more to culture or genes, and an important component of non-rational behavior is involved. Therefore there is not a well-defined equilibrium. A similar situation happens with (i), some types of killings of women.

Implications

Given a formal institutional vacuum, the incentive structure (e.g. of drug business), and the social structure (e.g. gang activity), the outcome is massive killings (a sort of “wild west”). To reduce the killing building a set of formal institutions is key. Working on the side of incentives (e.g. legalizing drugs) reduces “only” (a) and (b).