Game theory: what is it?

Theoretical models on decision making are very useful for sciences such as psychology, economics or politics as they help to predict the behavior of people in a large number of situations interactive.

Among these models stands out game theory, which consists of the analysis of decisions taken by the different actors in conflicts and in situations in which they can obtain benefits or damages depending on what other people involved do.

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What is game theory?

We can define game theory as the mathematical study of situations in which an individual has to make a decision taking into account the choices others make. At present this concept is used very frequently to name the theoretical models on rational decision making.

Within this framework we define as "game" any structured situation in which pre-established rewards or incentives can be obtained and that involves several people or other rational entities, such as artificial intelligence or animals. In general, we could say that games are similar to conflicts.

Following this definition, games constantly appear in everyday life. Thus, game theory is not only useful for predicting the behavior of people who participate in a game of cards, but also to analyze the price competition between two stores that are on the same street, as well as for many other situations.

Game theory can be considered a branch of economics or mathematics, specifically statistics. Given its wide scope, it has been used in many fields, such as psychology, economics, science politics, biology, philosophy, logic and computer science, to name a few examples featured.

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History and developments

This model began to consolidate thanks to the contributions of the Hungarian mathematician John von Neumann, or Neumann János Lajos, in his native language. This author published in 1928 an article entitled "On the theory of strategy games" and in 1944 the book "Game theory and economic behavior", together with Oskar Morgenstern.

Neuman's work focused on zero sum games, that is, those in which the benefit obtained by one or more of the actors is equivalent to the losses suffered by the rest of the participants.

Game theory would later come to be applied more broadly to many different games, both cooperative and non-cooperative. The American mathematician John Nash described what would become known as a “Nash equilibrium”., according to which if all players follow an optimal strategy, none of them will benefit if only their own changes.

Many theorists believe that the contributions of game theory have refuted the basic tenet of Adam Smith's economic liberalism, that is, that the search for individual benefit leads to the collective: according to the authors that we have mentioned, it is precisely selfishness that breaks the economic balance and generates situations that are not optimal.

game examples

Within game theory there are many models that have been used to exemplify and study rational decision making in interactive situations. In this section we will describe some of the most famous.

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1. prisoner's dilemma

The well-known prisoner's dilemma tries to exemplify the reasons that lead rational people to choose not to cooperate with each other. Its creators were the mathematicians Merrill Flood and Melvin Dresher.

This dilemma poses that two criminals are arrested by the police in connection with a specific offence. Separately, they are informed that if neither of them rats out the other as the perpetrator of the crime, they will both go to jail for 1 year; if one of them betrays the second but the latter remains silent, the informer will go free and the other will serve a 3-year sentence; if they accuse each other, both will receive a sentence of 2 years.

The most rational decision would be to choose betrayal, since it carries greater benefits. However, various studies based on the prisoner's dilemma have shown that people have a certain bias towards cooperation in situations like this.

2. The Monty Hall problem

Monty Hall was the host of the American television game show "Let's Make a Deal." This mathematical problem was popularized from a letter sent to a magazine.

The premise of the Monty Hall dilemma states that the person who is contesting on a television program must choose between three doors. Behind one of them is a car, while behind the other two are goats.

After the contestant chooses one of the doors, the presenter opens one of the remaining two; a goat appears He then asks the contestant if he wants to choose the other door instead of the initial one.

Although intuitively it seems that changing the door does not increase the chances of winning the car, the truth is that if the contestant maintains his original choice, he will have a ⅓ chance of obtaining the prize and if he changes it, the probability will be ⅔. This problem has served to illustrate the reluctance of people to change their beliefs even though they are refutedthrough logic.

3. The hawk and the dove (or “the hen”)

The hawk-dove model analyzes conflicts between individuals or groups that maintain aggressive strategies and others that are more peaceful. If both players adopt an aggressive attitude (hawk), the result will be very negative for both, while if only one of them does it, he will win and the second player will be harmed to a degree moderate.

In this case, whoever chooses first wins: in all probability he will choose the hawk strategy, since he knows that your opponent will be forced to choose the peaceful attitude (pigeon or hen) to minimize the costs.

This model has been frequently applied to politics. For example, imagine two military powers in cold war situation; if one of them threatens the other with a nuclear missile attack, the opponent should surrender to avoid a situation of mutual assured destruction, more detrimental than giving in to the demands of the rival.

Limitations of this area of ​​research

Due to its characteristics, game theory is useful as a research framework to develop strategies practically in any scale, from the behavior of individual people to geopolitical decision-making by State.

However, It must not be forgotten that it is not intended as a means through which to predict human behavior.; After all, the members of our species are not characterized by always acting rationally, and we never do so based on fixed and relatively easy to control rules.