Game Theory: What Does It Consist Of And In Which Areas Is It Applied?

This area of ​​research focuses on the study of logical decision making.

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

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

What is game theory?

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

Within this framework, we define a “game” as 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 intelligences or animals. In a general way, we could say that games are similar to conflicts.

Following this definition, games appear constantly in everyday life. Thus, game theory is not only useful for predicting the behavior of people participating in a card game, but also for analyzing price competition between two stores 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, political science, biology, philosophy, logic, and computer science, to name a few prominent examples.

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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.

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

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

Many theorists think that the contributions of game theory have refuted the basic principle of Adam Smith’s economic liberalism, that is, that the search for individual benefit leads to the collective: according to the authors we have mentioned, it is precisely selfishness that breaks the economic balance and generates non-optimal situations.

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. The prisoner’s dilemma

The well-known prisoner’s dilemma tries to exemplify the motives 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 apprehended by the police in relation to a specific crime. Separately, they are informed that if neither of them reports on 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 snitch 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 treason, since it brings greater benefits. However, various studies that are 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 contest “Let’s Make a Deal” (“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 competing in a television program must choose between three doors. Behind one of them is a car, while behind the other two there are goats.

After the contestant chooses one of the doors, the presenter opens one of the remaining two; a goat appears. Then ask the contestant if they want 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 keeps his original choice, he will have a ⅓ probability of winning 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 despite being refuted by 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 moderate degree.

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

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

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