Drug Hoarding and 'Prisoner's Dilemma'

Dilemmas often arise when people feel vulnerable. A case in point is the situation regarding the drug Ciprofloxacin, which some are stockpiling more to combat anxiety than to ward off anthrax.

The benefit of these purchases is a feeling of greater personal security, but one social cost is that Cipro may be in short supply if and when it's needed in large quantities. Another social cost is the increased bacterial resistance to the antibiotic that is likely to result from its widespread use.

The Prisoner's Dilemma

The so-called prisoner's dilemma is often used to model such conflicts. The dilemma owes its name to the scenario wherein two men suspected of a burglary are arrested in the course of committing some minor offense. They're separated and interrogated, and each is given the choice of confessing to the burglary and implicating his partner, or remaining silent.

If they both remain silent, they'll each receive only one year in prison. If one confesses and the other doesn't, the one who confesses will be rewarded by being let go, while the other one will receive a five-year term. If they both confess, they can both expect to spend three years in prison. The cooperative option is thus to remain silent, while the individualist option is to confess.

The dilemma is that what's best for them as a pair, to remain silent and spend a year in prison, leaves each of them open to the worst possibility, being a patsy and spending five years in prison. As a result they'll probably both confess and both spend three years in prison.

The Impact of Many Small Decisions

Most of us aren't crime suspects, but the dilemma provides the logical skeleton for many situations we do face everyday in real life. Whether we're competitors conducting business, spouses negotiating understandings, or anxious citizens vying for antibiotics, our choices can often be phrased in terms of the prisoner's dilemma. The two parties involved will often be better off as a pair if each resists the temptation to go it alone and instead cooperates with or remains loyal to the other person. Both parties' pursuing their own interests exclusively leads to a worse outcome than does cooperation.

This two-person prisoner's dilemma situation can be extended to many people, each having the choice whether to make a very small contribution to the public good or a much larger one to his or her own private gain. These small contributions add up, however, and society as a whole is better if more people take the cooperative option. This many-party prisoner's dilemma, useful in dealing with environmental goods such as clean air and water, is most relevant to the situation regarding Cipro.

If we refrain from buying our own supplies of Cipro, there will be more available in any emergency and the bacteria that constitute our common environment will not have as many tutorials to help them learn how to outwit the antibiotics.

Minuscule Risk

Alas, this is not to say that buying Cipro in anticipation of a possible emergency never makes sense, especially if one believes that the conditions of the prisoner's dilemma simply do not apply or that the public health system will not be up to the job in an emergency.

The best way public health people can minimize hoarding is to repeatedly stress that there is not yet such an emergency. And short of an unpredictable and improbable scientific breakthrough by a scientist in the employ of terrorists, the risk from anthrax is tiny.

Nearly 700 million pieces of mail are delivered daily and there have been only a handful of cases, almost all of them treated successfully. By contrast, nearly three quarters of a million Americans die annually from heart and circulatory diseases, around half a million from various forms of cancer, and more than 40,000 in car accidents. Even the much-derided and now almost idyllic-seeming shark menace has resulted in more deaths.

(Incidentally, a positive spin on the anthrax-laden letters is that they may indicate that the perpetrators don't have anything more virulent. Why would they warn us with isolated missives if they were capable of something much more horrific? The terrorists who attacked the World Trade Center did not first crash small Cessna planes into the towers as a prelude to doing so with jumbo jets.)

Another way to limit private stockpiling is for authorities, preferably scientists rather than politicians, to clearly proclaim that penicillin and doxycycline are also effective in combatting anthrax and that there is no shortage of these drugs. Finally, if and when much more Cipro is deemed necessary, government officials can always break the drug's patent, as Canada has done prematurely, and go to generic versions of the drug.

The bottom line is that private stockpiling of antibiotics makes no sense for most people. Nevertheless, for the relatively few who feel especially vulnerable — because of their psychology, physical location, or occupation — buying the drugs is not an irrational way to increase their feeling of security (as long as they refrain from taking them without a very good reason to suspect exposure).

The hysteria generated by the few anthrax-laden letters is dangerous and counter-productive. Resisting it is almost a patriotic duty, and anything that helps to do so is a good thing.

Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears every month.