The Omnipresent Prisoner’s Dilemma

Introduction

Originally proposed by mathematicians in the mid-20^th century, the Prisoner’s Dilemma is an amazingly simple framework that describes an incredibly powerful phenomenon that pervades almost every aspect of human existence. The game goes something like this:

Two men are arrested for a crime they allegedly committed together. The police arrest both men simultaneously and bring them separately to the police station, holding them in separate rooms, unable to communicate with each other. The police and prosecutors believe the men are guilty but only have enough evidence for a lesser charge. They, in separate conversations, give each of the men a choice:^[1]

As a unit, the optional decision for the group is for both men to stay silent. They will each get one year (a total of two for the group).  However, in real life, each man faces a more complex decision. If the first prisoner confesses and implicates his accomplice, he will either get away scot-free (if his accomplice doesn’t confess) or two years (if he does). If the first prisoner stays silent, he will either serve only one year (if the accomplice does the same) or three years (if the accomplice confesses). This can be represented by a very simple matrix:

With some form of coordination/communication – and complete trust – between the men, undoubtedly each would stay silent and take the one year each. However, in real life each man worries that the other man will betray him, and in an effort to minimize his downside (i.e., avoid the big three-year sentence), he will likely opt to confess. The result is that both men confess, and each gets two years in prison. Effectively, as a group they have reached a sub-optimal result, getting collectively four years in a prison. These were entirely rational decisions by each prisoner, but irrational for the pair.

There are many other ways to describe the same phenomenon – another common one is called the Diner’s Dilemma. This is a simulation where a bunch of friends go out to dinner together and agree beforehand to split the check equally. From a financial point of view, it would be in the group’s interest for each diner to order the cheapest possible dish. However, in practice (assuming no discussion and coordination among the diners about their specific menu choices), each diner realizes that if they order a more expensive dish (presumably one they wouldn’t have ordered if they were dining on their own), the extra cost would be shared among the whole group. In this case, each diner makes the same calculation and orders an expensive dish, with the result being a much higher total cost and thus an individual bill more than each wanted to spend. Again, the group collectively chose the sub-optimal decision even though it appeared as if each individual was making a rational decision in his/her own self-interest. 

Note that the Prisoner’s Dilemma construct looks at the “optimal” outcome from the point of view of the participants (i.e. prisoners or diners), irrespective whether we as a larger society think of it as a better outcome, morally or economically. 

In each of these examples, the affected parties could have chosen the optimal decision for the group if either they could (a) communicate and completely trust each other not to defect from the group, or (b) had an external party or force to mandate a decision for them. As one can imagine, this could be a role for government, often in an effort to in fact support capitalism and the optimal allocation of resources. 

The Dilemma in Practice

If the very premise of free market economics is that individual, self-interested, rational decisions collectively create the optional allocations for the group, then the Prisoner’s Dilemma represents an exception where the exact opposite is true. Even though we may not care much if real-life prisoners are coerced to confess to crimes, we probably underappreciate the omnipresence of the Prisoner’s Dilemma in our marketplace. 

It can be argued that almost all laws are meant to create a societal contract to prevent people from acting in their own self-interest when collectively this self-interest erodes the interests of the group. As a very simple example, if stealing were not illegal, we’d all have a very strong incentive to steal, because we’d think that everyone else is doing it. In the absence of a law and enforcement mechanism to prevent (or at least minimize) theft, an unrealistic amount of collective trust would be required for each of us to believe that no one else will steal. A more useful example may be paying our income taxes, as studies have shown that approximately 10% of Americans believe it’s okay to cheat on their taxes.^[2] No doubt this is at least in part fueled by a belief that others likely cheat. Cheating on one’s taxes is the equivalent of the prisoner defecting from the group. It serves one’s personal interest (assuming one doesn’t get caught), but if we all did it, we’d be collectively worse off versus the optimal outcome if none of us did it. 

Another fitting example would be doping in sports, whether it be Major League Baseball, the Olympics, or professional cycling. Lance Armstrong admitted that, in part, the impetus for taking performance-enhancing drugs was his belief that “everyone else” was doing it and the competitive disadvantage he would have by not. He and the other cyclists were just more prisoners defecting from the group.

The Prisoner’s Dilemma in its broadest abstraction also applies to analysis of public goods and externalities. If a society believes that pollution is harmful,^[3] then in order to maximize the value to the whole (by minimizing pollution), it either has to be regulated by an enforcing agency (e.g. a federal or state government) or it has to be regulated by a private agreement among polluters, in essence a trust among the prisoners. As the latter is often extremely difficult to effectuate, the practical solution is government regulation. Thus, regulation for this purpose is designed to provide the framework for prisoners to not defect from the group and therefore create a more optimal allocation of resources. There are certainly cases where an industry can self-regulate and can largely uphold this trusted agreement among them (e.g. MPAA movie ratings – the industry has created its own mechanisms for penalizing movie producers that do not adhere to the ratings system), but this is effectively just another type of framework imposed on this group of companies to prevent defecting from the group.

Locally, our states, counties, and towns are countering the effects of the Prisoner’s Dilemma inherently as part of their domain. Local zoning and related laws, for example, are effectively a community’s framework for enforcing an agreement – a good collusion, e.g. to only use land for specific uses. In the absence of such an enforceable agreement, each homeowner (or business) would have an incentive to defect from the group and build a multi-story structure that would cast a shadow, literally and figuratively, over its neighbors.

The Prisoner’s Dilemma isn’t all bad – sometimes we prefer a suboptimal outcome for the participants. In the case of our allegorical prisoners, we’re actually happy (assuming they are indeed guilty) that they can’t collude and come to an “optimal” solution for them. Any time the participants in this dilemma are bad actors, then the phenomenon of the Prisoner’s Dilemma actually works to our advantage. From an economic point of view, we could have bad actors – often companies – that are working counter to the principles and benefits of the free market. This can manifest from deliberately stifled competition among corporate rivals. For example, as there are both legal and illegal ways for companies to coordinate pricing strategies,^[4] a group of would-be competitors may be able to reach an “optimal” outcome for the group ensuring that all keep their prices high. However, the Prisoner’s Dilemma phenomenon gives an incentive for each competitor to lower prices (and defect from the group), creating an outcome that is better for consumers and for capitalism. One of the most dramatic examples of this is Russia and OPEC. As a cartel, OPEC is designed so that the members can collude to manipulate oil supply and prices to the benefit of the whole group. If it is working as designed, OPEC is an example of the prisoners cooperating. However, in one of many examples in its history of a member defecting from the group, Russia decided in March 2020 to refuse to reduce oil production. This decision was in their own short-term interest, but the subsequent drop in oil prices led to a sub-optimal outcome for the group. In this case, however, the Prisoner’s Dilemma serves capitalism, as OPEC is essentially a set of bad actors thwarting free market economics. 

Health and the COVID Crisis

Health care is an interesting case study as there are many examples where making decisions about one’s own health directly or indirectly affects others.^[5] One of the most explicit examples of these interrelationships – and the applicability of the Prisoner’s Dilemma framework – is vaccinations. For a communicable disease, the action of any individual directly affects others. Even if one were to assume that there is any risk to one’s own health by getting a vaccine,^[6] the choice to vaccinate is a classical prisoners dilemma. If one felt that the risk of vaccinating was greater than the benefit, then it’s in that person’s interest to eschew a vaccination while hoping everyone else gets one. A choice to not vaccinate oneself or one’s children is effectively a defection from the group in a Prisoner’s Dilemma. Of course, if everyone defected from the group in this way, we’d have a population where no one was vaccinated, and a disease would run rampant. Even with a partial defection where a relatively small subset of people go without, deadly consequences could follow.^[7]

As this is written, we are in the middle of the COVID-19 crisis, the most severe health and economic crisis the world has seen in a century. Because of the communicability of the virus, everyone’s actions affect many others. Yet, governments and society have struggled with policies about everything from business closures to mask and distancing guidelines to vaccine mandates. Knowing that, regardless of the law, people will defect from the group (and defect from the societal compact to protect each other), governments are in the awkward position balancing the creation of rules that both minimize the overall health risks to the community but also trying to minimize the likelihood that a significant number of individuals would indeed defect from the group.

When the current crisis started, one of the biggest stories (besides the infections and deaths) was the lack of toilet paper in stores. Although there is no rational evidence that the existence of the virus would require anyone to use any more toilet paper than usual, there was a run on toilet paper causing shortages for weeks across the country.^[8] This hoarding behavior was based on nothing more than the assumption that everyone else was going to do it – a mass defection in the Prisoner’s Dilemma. Bank runs that happened after the stock market crash of 1929 created the same phenomenon – if enough individuals thought that everyone else was going to take their money out of the bank, then eventually everyone would rush to take their money out of the bank, self-fulfilling that prophecy. In both examples, many of us defected from the contract that we had with our neighbors. After the 1929 crash, the U.S. created the Federal Deposit Insurance Corporation to guarantee that individuals’ money would be protected – the external force required to prevent (or at least mitigate) such defections in the future.

In general, most Public Goods – those goods/services where the value is so dispersed among the citizenry that it is impossible or cost-prohibitive to measure the value provided to each person and/or extremely difficult to collect payment for such value – are managed in such a way to avoid the Prisoner’s Dilemma. In developed economies, we rely much more on government-provided services like public safety, infrastructure, and public education. On an individual level, there could be an incentive for each of us to defect from the group and (if we could afford it) provide our own private security or private roads, but it would a terribly inefficient use of resources and result in a far worse economic outcome for all. Therefore, a good government, properly resourced, steps in to provide these public goods, which are often far from perfect but almost always more efficient from an overall allocation of resource point of view.

Unexpected Results

One of the most interesting applications of the Prisoner’s Dilemma is how it can turn microeconomics on its ear in those situations where entities become “forced” to act counter to what they would have chosen, yet in doing so, wind up creating an outcome consistent with their long-term best interest.

A classic example of this is mileage standards for automobiles. The main justification for imposing standards on vehicle fuel efficiency is to deal with another problem of capitalism – the negative externality, in this case the health and economic costs of burning fossil fuels. It certainly succeeds in that goal (higher MPH standards lead to less carbon in the atmosphere), but the classic argument against raising standards is that it will increase costs for auto manufacturers and therefore consumers who purchase those autos. Once again, the Prisoner’s Dilemma can help explain why this is so. In the absence of any regulation forcing auto makers to improve fuel efficiency, there is very little incentive for any one company to unilaterally improve their standards. The benefit may, in the short-term, seem very minor as consumers generally fail to calculate the long-term economic benefit of spending less on gasoline,^[9] and the company may need to make other compromises in the car in terms of size, style, or perhaps increased costs – all of which will be perceived to give them a relative disadvantage against their competitors. However, if every manufacturer is forced to a higher efficiency standard, no individual manufacturer has this problem anymore. With all of them working to design cars with better fuel efficiency, they are forced to innovate, and with everyone innovating (and copying innovations), the entire industry can provide better products at lower prices. Additionally, consumers become more aware of fuel efficiency, start to better calculate the benefits to them, and aesthetic tastes may even evolve to favor more aerodynamic cars, for example. So, it is this regulation which forces a certain collective behavior, in effect making it impossible to “defect” from the group back to the status quo, which counterintuitively provided less incentive for innovation.^[10]

Conclusion

Darwinian evolution is based on the natural selection of variations in species that enables one member of that species to adapt, survive, and reproduce better than all others. It is inherently an individual competition, akin to a free market of developmental biology. Yet, in many species, particularly primates, behaviors have evolved over time that seem contrary to this evolutionary competition. One such example is apes’ performing “social grooming” where each member of a group will conduct this seemingly altruistic act of grooming another member, cleaning him/her of dirt and insects and otherwise promoting their health. The apes have a social contract, one that is often enforced by instincts, teachings, and perhaps more heavy-handedly by a senior member of the clan. By not defecting from the group, each ape creates optimal value for all other apes. Evolution was therefore not solely an individual competition, but rather one that also championed these social traits to optimize benefits to the entire species. It should therefore come as no surprise that humans, as one of the ultimate social species, cannot separate any individual’s welfare from that of others. 

Analogously, capitalism is a great starting framework for allocating economic resources among an incredibly diverse group of producers and consumers, but it cultivates better outcomes for all when it takes into account the obvious connections among these economic players. The Prisoner’s Dilemma is one very powerful construct to understand and appreciate these connections and make policy decisions that actually enhance both the inherent social contract among humans as well as bestow better economic outcomes than the free market would provide alone. One cannot understand capitalism – and certainly the proper role of government in a capitalistic society – without applying the framework of the Prisoner’s Dilemma. 

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^[1] For the purpose of this game, we must ignore the fact that in real life prisoners have certain rights (like access to an attorney) and that the police and prosecutors may not be able to actually construct such a deal.

^[2] IRS 2018 Data Book

^[3] Besides the health and lifestyle costs, there are very clear short- and long-term economic costs to this externality – the problem is often is that the costs aren’t measured and almost always those costs are not internalized, meaning added the price of the product/service

^[4] Although in the U.S. there are antitrust laws that can prevent much anticompetitive behavior among companies, there are still a number of ways companies can indirectly coordinate through price signaling, exclusivity agreements, product dumping, etc.

^[5] Which is, unsurprisingly, why most countries recognize that they are not served well by a free market health care system either in terms of financial efficiency or medical outcomes.

^[6] A belief that is largely discredited with the exception of a very small subset individuals who indeed are not recommended to get certain vaccines for medical reasons.

^[7] The 2018-2019 measles outbreak in the U.S., for example.

^[8] Interesting, many cleaning products had a more justifiable run – those were products with a far greater utility during a pandemic, and ones that would be used up faster

^[9] Another example of consumers inability to act rationally in their own interest

^[10] This argument assumes the requirements are reasonably achievable. A mandate to have all cars get 200 MPH next year would not achieve the desired results