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 stands out **game theory, which consists of the analysis of decisions ** that different actors take in conflicts and in situations in which they can obtain benefits or harm depending on what other people involved do.

## 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 ** Currently this concept is very frequently used to name theoretical models of rational decision making.

Within this framework we define “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 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 participating in a card game, but also for analyzing 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, political science, biology, philosophy, logic and computer science, to name a few notable examples.

## 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 an article titled “On the theory of strategy games” in 1928 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 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 be known as “Nash equilibrium” ** according to which if all players follow an optimal strategy, none of them will benefit if only their own strategy changes.

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

## Examples of games

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.

### 1. The 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 relation to a specific crime. Separately, they are informed that if neither of them betrays 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 maintains silence, the snitch will be free and the other will serve a 3-year sentence; If they accuse each other, both will receive a 2-year sentence.

The most rational decision would be to choose betrayal, since it brings 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 became popular after a letter sent to a magazine.

The premise of the Monty Hall dilemma states that the person who is competing on a television show **You must choose between three doors ** Behind one of them there 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. 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 probability of winning the prize and if he changes it the probability will be ⅔. This problem has served to illustrate people’s reluctance to modify their beliefs. **even though they are refuted ** **through logic **

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

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 so he will win and the second player will be harmed to a moderate degree.

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

This model has frequently been applied to politics. For example, let’s 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 mutual assured destruction, which is more damaging than giving in to the rival’s demands.

## The limitations of this area of research

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

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