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Game theory: what does it consist of and in what fields does it apply?

Game theory: what does it consist of and in what fields does it apply?

March 30, 2024

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

Among these models, it stands out game theory, which is the analysis of decisions that the different actors take 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 the theory of games?

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 that others make . Currently, this concept is used very frequently to refer to 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 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 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, political science, biology, philosophy, logic and computer science, to mention a few outstanding examples.

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History and developments

This model began to consolidate thanks to the Contributions by 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 "Theory of games and economic behavior", together with Oskar Morgenstern.

The work of Neumann 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.

Later game theory would be applied more broadly to many different games, both cooperative and non-cooperative. 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 they change only their own.

Many theorists think that the contributions of game theory have refuted the basic principle of economic liberalism by Adam Smith , 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.

Examples of games

Within the theory of games 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 dilemma of the prisoner 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 imprisoned 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, both will go to jail for 1 year; if one of them betrays the second but he keeps silence, the informer will be free and the other will serve a sentence of 3 years; if they accuse each other, both will receive a sentence of 2 years.

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

2. The problem of Monty Hall

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

The premise of the dilemma of Monty Hall argues that the person who is competing in a television program 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. Next ask 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 ⅓ probability of winning the prize and if he changes the probability it will be ⅔. This problem has served to illustrate the reluctance of people to change their beliefs even though they are refuted through logic .

3. The falcon and the dove (or "the hen")

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

In this case, the one who 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 the costs.

This model has been applied frequently to politics. For example, imagine two military powers in a situation of cold war ; 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 harmful than yielding to the rival's demands.

Game Theory: The Science of Decision-Making (March 2024).

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