Game theory is a branch of mathematics that studies the behavior of individuals when they interact with each other through a series of well-defined rules. The so-called prisoner's dilemma is one of the most common examples of this type of problem, with hundreds of applications in everyday life. At its core, it raises the question of whether it is more profitable to be altruistic or, on the contrary, whether the highly selfish are the ones who ultimately come out ahead. The results are surprising.
Despite what its name might suggest, the so-called game theory is a serious matter. It is a branch of mathematics that deals with how to win in games that have well-defined rules. From the perspective of this theory, a game consists of a set of players, a set of moves (or strategies) available to those players, and a series of rewards for each combination of strategies.
Many real-world situations can be modeled as if they were a game and resolved — or at least analyzed — through the use of game theory. This is especially interesting in fields like biology or economics, since the correct application of this tool allows optimal results to be obtained even when the costs and benefits of each option are not fixed in advance but depend on the choices of other individuals.
A well-known example of applying game theory to real life is the prisoner's dilemma. This “game” was popularized by mathematician Albert W. Tucker. Despite the simplicity of its approach, this dilemma has implications that are useful for understanding the nature of human cooperation. The classic statement of the prisoner's dilemma is as follows:
The police have just arrested two suspects of a crime. Not enough evidence has been found to convict them, and after separating them, a police officer visits each one and offers them the same deal. If one confesses and the accomplice does not, the accomplice will be sentenced to ten years in prison while the informant will be released. Conversely, if he remains silent and the accomplice confesses, the first will receive that sentence and the accomplice will be the one to go free. But if both confess to the crime, each will receive a lesser sentence of only six years. If neither confesses, due to lack of evidence, they will spend no more than six months in jail accused of a lesser charge.
The time they will spend in prison basically depends on how supportive or selfish the two criminals are. Each prisoner has two options: cooperate with his accomplice by remaining silent and both go free in six months, or betray him by confessing to be released immediately while his “partner” spends 10 years behind bars. What makes the dilemma interesting is the fact that the result of each choice depends on the accomplice's choice, and each one does not know what the other has chosen, since they are separated.
Let's start by assuming that both are completely selfish and have as their only goal reducing the time they will spend detained. Each prisoner could suppose that the other has chosen to cooperate by keeping his mouth shut to get out in six months. This makes the temptation to be the first to confess enormous, since it would mean immediate freedom and a 10-year sentence for his accomplice. Of course, the other detainee is surely reasoning in the same way, looking for a way to get out immediately. If both are selfish, the possibility that both confess and spend 6 years in prison is very high.
On the contrary, interest in the common good can yield much better results. Leaving aside the fact that two criminals are unlikely to have any interest in things like altruism, the truth is that trust in the behavior of the other can get the best result. From the point of view of cold logic, confessing is the dominant strategy for both players. Whatever the choice of the other player, they can always reduce their sentence by confessing. But on the other hand, this leads to a regular result if both make that decision. This is the crux of the dilemma.
The result of individual interactions produces a result that is not optimal, although there is such a situation where the prospects of one of the detainees can improve without implying a worsening for the other. In fact, if both remain silent they receive a total sentence of one year (six months each), while in the other cases they would receive 10 (if only one confesses and goes free) or 12 (six years each if both confessed immediately).
It may seem that the prisoner's dilemma is nothing more than a mathematical pastime. However, there are many examples of human (and natural) interactions that can be analyzed in the same way. This makes the dilemma of interest to economics, political science, sociology, biological sciences, and almost any field of knowledge you can imagine. For example, within the field of international relations, the prisoner's dilemma scenario serves to illustrate the situation in which two states involved in an arms race find themselves.
Both countries have two options: either increase military spending, or sign an agreement to reduce their armaments. Since neither can be completely sure that the other will abide by the agreement, both end up deciding on military expansion. The irony is that both states seem to act rationally, but the result is completely irrational. Humanity as a whole would benefit from altruistic behavior, but selfishness usually wins the game, embarking us on delusions like Mutual Assured Destruction.
After having posed the prisoner's dilemma we can draw some conclusions. In the field of ethics, for example, one of the most ancient questions is why do good? This was already worrying Plato, and it reappears throughout history in the most diverse forms. The prisoner's dilemma helps us find a simple and practical answer: when we all seek the interest of the group, we obtain more benefits than when we seek the best result individually. In short, the best way to get the best for each one is to do what is best for everyone. Morality, it seems, is a good business. Interesting, right?
