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

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

Theoretical models of 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 interactive situations.

Among these models, the following stand out game theory, which consists of the analysis of the decisions made by the different The analysis of the decisions made by the 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 situations in which an individual has to make a decision taking into account the choices made by others. Nowadays this concept is very frequently used to refer to theoretical models of rational decision making.

Within this framework, we define a "game" as any structured situation in which predefined rewards or incentives can be structured situation in which pre-established rewards or incentives can be obtained, and which involves and involving 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 the price competition between two stores in the same street, as well as for many other situations.

Game theory can be considered a branch of economics or mathematics, in particular statistics.. Given its broad scope, it has been used in many fields, such as psychology, economics, political science, biology, philosophy, logic and computer science, to mention some prominent examples.

• You may be interested in "Are we rational or emotional beings?"

History and developments

This model began to consolidate thanks to the contributions of the Hungarian mathematician 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 gamesthat is, those in which the profit obtained by one or more of the players is equivalent to the losses suffered by the other participants.

Later, game theory would come to be applied more broadly to many different games, both cooperative and non-cooperative. The American mathematician John Nash described what would come to be known as the "Nash equilibrium", whereby if all players follow an optimal strategyaccording 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 disproved the basic principle of economic liberalism of the basic principle of Adam Smith's economic liberalism, i.e., that the search for the optimal strategythat is, that the pursuit of individual profit leads to collective profit: according to the aforementioned authors, it is precisely selfishness that breaks the economic equilibrium and generates sub-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 ones.

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 posits that two criminals are apprehended by the police in connection with a crime. by the police in connection with a particular 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 the latter keeps silent, the snitch will go 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 carries greater benefits. However, several studies based on the prisoner's dilemma have shown that people have a certain bias towards cooperation. people have a certain bias toward cooperation in situations like this one. in situations like this.

2. The Monty Hall problem

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

The premise of Monty Hall's dilemma is that the person who is competing in a television show 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 other two doors; 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 keeps his original choice he will have ⅓ of probability 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 refuted by means of logic.

3. The hawk and the dove (or "the chicken").

The hawk-dove model analyzes conflicts between individuals or groups who maintain aggressive groups that maintain aggressive strategies and others that are more pacific.. 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 probability he will choose the hawkish strategy, since he knows that his opponent will be forced to choose the peaceful attitude (pigeon or chicken) to minimize costs.

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

The limitations of this field of research

Because of its characteristics, game theory is useful as a research framework for developing strategies on virtually any scale, from the behavior of individual people to geopolitical decision making by states.

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

Bibliographical references:

• Beck, J. (2008). Combinatorial Games: Tic-Tac-Toe Theory. Cambridge: Cambridge University Press.
• Bewersdorff, J. (2005). Luck, logic, and white lies: the mathematics of games. A K Peters, Ltd.
• Leonard, R. (2010). Von Neumann, Morgenstern, and the Creation of Game Theory. New York: Cambridge University Press.
• Myerson, R.B. (1991). Game Theory: Analysis of Conflict. Harvard: Harvard University Press.
• Sanfey, A.G. (2007). Social Decision-Making: Insights from Game Theory and Neuroscience. Science, 318(5850): pp. 598 - 602.