The Fallacy of the Prisoners’ Dilemma

The prisoners’ dilemma, based on a paper written by Merrill Flood and Melvin Dresher in 1950, has become the paradigmatic example of game theory, which is presently being applied to more and more academic disciplines and areas of research. A very common tendency with new theories or models is that they are applied indiscriminately to more and more areas of study.[1] This is due to the fact that researchers imitate what other researchers are doing. It is only after a longer period of time that it becomes apparent that some of these applications were inaccurate, inappropriate, or wrong. For example, the evolutionary geneticist Richard Dawkins is profusely enthusiastic in touting the global applicability of game theory. In his book The Selfish Gene, he declares,

[American political scientist Robert] Axelrod, like many political scientists, economists, mathematicians and psychologists, was fascinated by a simple gambling game called Prisoner’s Dilemma. It is so simple that I have known clever men misunderstand it completely, thinking that there must be more to it! But its simplicity is deceptive. Whole shelves in libraries are devoted to the ramifications of this beguiling game. Many influential people think it holds the key to strategic defence planning, and that we should study it to prevent a third world war. As a biologist, I agree with Axelrod and [W. D.] Hamilton that many wild animals and plants are engaged in ceaseless games of Prisoner’s Dilemma, played out in evolutionary time.

[…] The more you think about it, the more you realize that life is riddled with Iterated [repeated] Prisoner’s Dilemma games, not just human life but animal and plant life too. Plant life? Yes, why not? Remember that we are not talking about conscious strategies (though at times we might be), but about strategies in the ‘Maynard Smithian” sense, strategies of the kind that genes might preprogram. Later we shall meet plants, various animals and even bacteria, all playing the game of Iterated Prisoner’s Dilemma.[2]

However, there is a significant problem with the prisoners’ dilemma, namely the fact that, in its later formulation by Albert W. Tucker,[3] it leaves out some pretty important determinants of whether a real-life prisoner – and not the imaginary prisoners postulated in the prisoners’ dilemma – will confess or not. In other words, in its attempt to model real-world human behaviours, this game-theory paradigm is seriously incomplete.

According to the Theory of Imitation, a prisoner is more likely to confess if one feels shame at one’s actions. Similarly, in non-criminal instances of wrongdoing, a person is more likely to accept blame or apologize for a wrong, injury, or offense if one feels ashamed or embarrassed by it. In contrast, a person is less likely to confess if one feels no shame and, instead, feels contempt towards one’s jailers or victim(s). In the case of prisoners, these are what are called “hardened criminals,” who often feel contempt towards society’s laws and rules, which is why they violate them with such regularity and equanimity. It is common for criminals to express contempt or loathing towards those who “squelch,” “rat,” “snitch,” or cooperate in other ways with the authorities. And since contempt can be imitated like other aspects of human behaviour, those who hear such scornful denunciations will be less likely to confess or cooperate if they are caught. Many professional or long-term criminals would never consider working in the future with a person who cooperates with the authorities, such as by giving evidence against them, since, by one’s actions, one has sided with the enemy. And in criminal organizations like the mafia, those who cooperate with the authorities are often summarily executed for having betrayed the organization.

What this means is that the payoffs in the prisoners’ dilemma, whether in reduced jail sentences or monetary rewards, are not the only things that matter in determining how the “players” will behave. In other words, the artificial simplicity posited by the prisoners’ dilemma differs from the more complex reality that it attempts to model. In culinary terms, this is comparable to preparing a classic dish like boeuf bourguignon while leaving out one or more of the main ingredients, such as the carrots or wine, and then claiming that it is in fact boeuf bourguignon. Similarly, although the prisoners’ dilemma claims that it correctly models real-world human behaviours, it leaves out some important determinants of people’s behaviours.

Contempt often does enter into negotiations and decision-making in general, such as during peace and labour union negotiations. When one side is scornful of the other, then reaching an agreement becomes much more difficult, and in some cases impossible. Another common example is divorce proceedings where one or both parties scorn the other party, with the result that they are unwilling to compromise, and they may do things in order to get back at the other person. In some cases, the replacement of a widely-scorned negotiator, such as a company boss who is scorned by the workers because of certain actions or decisions one has made in the past, with someone else may be critical to the two sides’ ability to reach an agreement. In addition, even if an agreement is reached, if the members of one of the sides scorn the other, then it makes the violation of the agreement more likely. These effects are due to the fact that contempt makes people uncooperative. In general, contempt makes people unwilling, and hence less likely, to imitate, follow, trust, believe, support, hire, work or do business with, vote for, or agree or cooperate with a scorned person or group of people.

Here is an example of a failure that resulted from the misapplication of game theory’s overly simplistic assumptions about human behaviour to the real world:

Economists’ attachment to particular modeling conventions—rational, forward-looking individuals, well-functioning markets, and so on—often leads them to overlook obvious conflicts with the world around them. Yale University game theorist Barry Nalebuff is more world-savvy than most, yet even he has gotten into trouble. Nalebuff and another game theorist found themselves in a cab late one night in Israel. The driver did not turn the meter on but promised them he would charge a lower price at the end of the ride than what the meter would have indicated. Nalebuff and his colleague had no reason to trust the driver. But they were game theorists and reasoned as follows: Once they had reached their destination, the driver would have very little bargaining power. He would have to accept pretty much what his passengers were willing to pay. So they decided that the driver’s offer was a good deal, and they went along. Once arriving at their destination, the driver requested 2,500 shekels. Nalebuff refused and offered 2,200 shekels instead. While Nalebuff was attempting to negotiate, the outraged driver locked the car, imprisoning his passengers inside, and drove at breakneck speed back to where he had picked them up. He kicked them to the curb, yelling, “See how far your 2,200 shekels will get you now.”

Standard game theory, it turned out, was a poor guide for what actually transpired.[4]

To understand the cab driver’s behaviour, we need to recognize that the two game-theorists’ decision to offer him a lower sum[5] than the one that the cab driver knew or believed was a fair amount for the distance driven provoked the driver’s contempt and anger. Viewed from the assumption of rationality, the cab driver’s behaviour makes no sense whatsoever: not only did he lose the 2,200 shekels that his passengers were willing to pay him, he lost both the gasoline and the time which he spent on the wasted trip, since, during that time, he might have found another passenger who was not a game theorist intent on saving a little money. Rather than being a net gain, which is what the trip would have been had he accepted the slightly lower offer, the trip was a net loss – an outcome that, according to game theorists, is simply not possible in such a situation because of their belief that all human beings are rational creatures. This is only one example of how economists and game theorists fail to understand the true causes of human behaviour.

Game theory models like the classic prisoners’ dilemma falsely assume that human beings are entirely free to choose which of the two or more actions they will take, without considering the effects on one’s behaviour of traditions, peer pressure, what those who are in one’s realm of influence will think of one’s decision, and so forth. Numerous are the historical examples of a people rejecting new innovations or practices that would clearly have been advantageous to them, simply because they went against their traditions. For example, vaccination was notoriously difficult to implement in areas where people were uneducated, and many gypsies have refused to settle down in one place because it would have meant abandoning their nomadic traditions. Presently, governments in some countries are having considerable difficulty in attempting to limit or reduce their country’s population by encouraging people to use some form of birth control, again because using birth control goes against their traditions or religion, which is another form of traditional behaviour. These examples show that, contrary to what game theorists and others assume, in many real-world situations, people are not entirely free to pursue the most rational outcome, or the outcome that is most advantageous to them – which, of course, contradicts the assumptions made by game theorists and others. The prisoners’ dilemma is simply another example of the mistaken philosophical belief that human beings are rational creatures that seek out the most logical or rational outcome in every situation in their lives, whether in terms of monetary payoffs, reduced prison sentences, greater pleasure or utility, and so on.

If we ask the question, “Why did Albert Tucker and his many imitators overlook these important determinants of whether a criminal will confess or not?”, I suspect the answer is that Tucker, along with the many others who have naively applied the prisoners’ dilemma to their particular area of study, had not spent any time in jail, and they did not know any prisoners personally. In addition, I doubt that these individuals bothered to ask any real prisoners or criminals how they would have behaved in the situation posited by this game.[6] In other words, neither Tucker nor his many imitators had any first-hand, or even second-hand, experience of actually being in prison and being faced with the situation posited by the prisoners’ dilemma. Instead, like many other researchers, they confidently proceeded according to their naive and ignorant assumptions, believing that they knew how a real prisoner would behave, namely, that all prisoners, like human beings in general, behave, in all times and places, like rational creatures.

What this means is that the conception held by Tucker and his many imitators of how prisoners would behave is about as accurate as the conceptions that people have more generally about a group of people they have never met and know little or nothing about. Most people realize that these kinds of cultural, religious, ethnic, or group stereotypes, conceptions, or generalizations are frequently wrong, incomplete, or outdated. To the extent that models like the prisoners’ dilemma differ from reality, they give researchers and others a distorted picture of reality, while they are unaware of this important fact.

Of course, since shame and contempt are uniquely human phenomena, the numerous applications of the prisoners’ dilemma to non-human domains or disciplines are not subject to this criticism. However, the fact that the original game-theory model has some pretty serious flaws and shortcomings should lead researchers to question whether it is appropriate to apply it to other areas of study. In other words, one should be wary of applying it in situations where it is not appropriate, and one should also be wary of those who, like Richard Dawkins, apply it indiscriminately with an immoderate enthusiasm. Similarly, in the past, logical or mathematical methods, whether the syllogism, reasoning from first principles, calculus, differential equations, statistics, or probability methods, were applied inappropriately by those who failed to understand their limitations in helping us to understand real-world phenomena.

In the case of economics, why has the application of game theory, and mathematical methods in general, produced so many harmful results? The answer is that the economists’ naive assumption that everything that matters is contained in the narrow confines of the game-theory payoff matrix, or can be quantified in other ways, is wrong. Economists’ fixation on those things that can be quantified and measured has rendered them completely blind to many other things that are also important. Traditions, and preserving their particular traditions, are important for many people. And yet, economists completely ignore traditions in their calculations, as well as in their recommendations about how people should behave. This is because one cannot quantify traditions and the attachment that people have to them. Although one could arbitrarily assign a monetary value or other numerical figure to a person’s attachment to one’s traditions, this way of proceeding attempts to subsume something that is non-monetary in the monetizing computations of economists. It is just as absurd as attempting to put a monetary figure on love. This explains why the imposition of free-market economic doctrines like free trade, privatization, specialization, and so forth, on numerous peoples around the world, has been so highly disruptive of their traditions.

What this means is that the economists’ assumption that everything that is important in life can be assigned a monetary value is wrong. Out of their overly simplified equations, theories, and considerations, they have left out important real-world determinants of our behaviours like traditions, shame or embarrassment, prestige, honour, social status, conformity, admiration, contempt, and consideration for others. And it is precisely for this reason that the recent dominance of economics as a generalized theory of human behaviour has caused so much harm, by leading many economists and their students astray, off the narrow and meandering path of truth – since truth most certainly is not a straight, unvarying path – and onto the vast barren wastelands of falsehood, error, deception, and misplaced confidence.

We can ask ourselves the following important questions: What are the characteristics of a good theory or model? And how can we distinguish good from bad theories and models?

All theories simplify the real world in order, so the hope goes, to help people to understand its operations. Similarly, no useful map is drawn precisely to scale or includes everything in the terrain which it aims to depict. However, as we have seen in the case of the prisoners’ dilemma, a model or theory will be wrong or misleading if it leaves out important elements, forces, or determinants of the things we want to understand, or, conversely, if it includes or emphasizes the wrong concepts, elements, forces, or determinants. Similarly, if a map leaves out an important geographical or urban feature like a river, lake, or highway, then it will obviously be incomplete and potentially misleading.

Just as, if one follows a faulty map, one will probably not arrive at one’s intended destination or find what one is looking for, acting or deciding based on an incorrect or incomplete theory will beget harmful, useless, foolish, or dangerous behaviours. A historical example is the four humours theory of human health and disease, which posited the existence of four humours in the body. When these humours are in balance, so the theory declared, one is in good health, but when they are out of balance, one is prone to sickness and disease. Hence, the useless practice of bloodletting resulted directly from this mistaken theory, as a way to restore the desired balance between the four bodily humours. A more recent example is communism, whose real-world effects differed greatly from the confident expectations of the theory’s adherents. Similarly, the application of economic prescriptions in the real world often produces results that differ from the expectations of the economic model’s or theory’s adherents, which demonstrates that the model or theory is either wrong or incomplete.

One can arbitrarily separate certain behaviours and declare that one will study only these behaviours, as economists have done in focusing solely on studying productive economic activities, and moreover, on only those activities that have a monetary value; but in doing so, one must be careful that this arbitrary separation does not blind one to other important determinants of the behaviours one is studying, something that many economists have not taken care to do. It is like declaring that one will focus solely on studying the motions of a certain part of one’s body like the hands, while completely ignoring what the rest of the body is doing, including the brain, heart, lungs, kidneys, liver, stomach, and legs. For obviously both the condition and motions of the hands will be influenced by these other body parts, since they form parts of one integrated whole.

With the advent of computer models or simulations, many people, including scientific researchers, are, in some cases, naively concluding that if a computer model based on certain assumptions is able to generate outcomes that closely approximate real-world observations, then that means the model is correct. But we would do well to recall that the Ptolemaic model of the heavens also did a fairly good job of explaining astronomical observations, as they existed at the time, and yet most people no longer accept it as true. Given the observations that astronomers had then, which were recorded entirely from the perspective of the Earth and without the aid of telescopes, the Ptolemaic theory of the heavens was not obviously false, as it appears to most people today. Similarly, some of the computer simulation models that give fairly good real-world approximations may also be based on one or more false assumptions.

Game-theory paradigms like the prisoners’ dilemma are based on the falsehood that human beings are rational creatures. It is time for the many imitating simpletons who apply logical models like the prisoners’ dilemma to reconsider whether this model does in fact provide a good fit with the phenomena which they are trying to understand, or whether their blind admiration for the model’s logical elegance has made them overlook important determinants of these and other real-world phenomena.

[1] Of course, this observation only applies to influential theories and models. Most models and theories do not achieve much success or influence, just like most other things, whether one is talking about books, films, clothing fashions, words or phrases, electronic products, inventions, or persons.

[2] The Selfish Gene by Richard Dawkins, pp. 203 and 208. Oxford University Press, Oxford, 2006.

[3] The discussion of the originators of the prisoners’ dilemma is made somewhat problematic due to the fact that, in the original paper written by Flood and Dresher, there was no mention of prisoners. It was Tucker who gave it its better-known criminal form and, in the process, rechristened it as the “prisoners’ dilemma.” However, game theorists, economists, and others regard the two most common forms, which involve payoffs in terms of shorter prison sentences or money, or some other desirable outcome or commodity, as being entirely interchangeable, a view with which I disagree.

[4] Economic Rules: The Rights and Wrongs of the Dismal Science by Dani Rodrik, chapter 3. W. W. Norton & Company, New York, 2015.

[5] This decision probably resulted from another frequently erroneous assumption made by economists, namely that all human beings are selfish maximizers of their utility. In this particular situation, this led the two game theorists to assume that the cab driver would have no scruples in trying to cheat two passengers whom he would probably never encounter again, and who, being foreigners, would not know what was a fair price for their trip.

[6] To demonstrate the fallacy of the prisoners’ dilemma, one could take a survey of prisoners and ask them a question such as the following: “What factors would determine whether you would be willing or unwilling to cooperate with the authorities, receiving a reduced prison sentence for cooperating, and a longer sentence for not cooperating?”