# Games theory

Game theory is a branch of mathematics and economics that studies the choice of the optimal behavior of an individual when the costs and benefits of each option are not fixed in advance, but depend on the choices of other individuals.

In economic life there are countless situations in which two or more people, companies or countries have to choose strategies and make decisions in which they are mutually affected. Game theory attempts to analyze these cases and is used especially in economics to study oligopoly and duopoly markets, in which two or more agents make decisions that jointly affect all participants.

This theory, which conceives individuals as homo economicus (understands that the player chooses the actions that best satisfy their objectives based on their beliefs), and in turn, shows how cooperation leads to the common good of the agents who perform it, while individual performance does not. One of the games most studied by game theory is the prisoner's dilemma.

## Origin of game theory

Game theory as a field of study came into being in 1928, when the mathematician John von Neuman published a series of analyzes. During this period, game theory studies focused primarily on cooperative game theory.

Game theory was gaining weight throughout the 1950s, when the first discussions of the prisoner's dilemma were established and the Nash equilibrium, the greatest exponent of non-cooperative games, was developed.

Over the last decades, game theory has been deepened, serving as the basis for making applications in various areas.

## Game Categories

There are thousands of games, such as Parcheesi, chess or basketball. All of them can be divided into different categories, let's see the main ones:

• Symmetrical or asymmetric: A symmetrical game is one in which the rewards and punishments of each player are the same. Examples of symmetrical games are the game of the hawk and the dove, the prisoner's dilemma, and the deer hunt, in their standard features. Most 2 × 2 games are symmetrical. In contrast, the ultimatum game and the dictator game are asymmetrical.
• Zero-sum or non-zero-sum games: When one player wins, the other loses exactly the same amount. Chess, go, poker, and the bear game are zero-sum games. Even the stock market is a zero-sum game (regardless of commissions). The prisoner's dilemma is a non-zero sum game, like football, since if it is tied, a point is won, but if it is won, three are added (if two were added when winning, as in the past, it would be a game of zero sum).
• Cooperative or non-cooperative games: Cooperative games are those in which two or more players form a team to achieve a goal, the optimal strategies for groups of individuals are analyzed, assuming that they can establish agreements with each other about the most appropriate strategies.
• Nash equilibrium: The final solution that is reached is an equilibrium in which neither player gains anything by modifying their strategy while the other or the others maintain theirs. That is, neither party can change its individual decision without making it worse.
• Simultaneous or sequential: In sequential games each player acts after another, while in simultaneous ones they act at the same time.
• Perfect or imperfect information: In perfect information games all players know what others have done before.

## Game theory applications

Game theory has many applications in different fields, highlighting economic science, political science, evolutionary biology or even philosophy.

Regarding the economy and business, although we understand by economy, the social science that studies how to manage the available resources, this in itself already provides all the ingredients for a game. Researchers in this branch of game theory have focused on studying the duopoly and oligopoly markets.

In political science Game theory has not had the same impact on political science as on economics. Perhaps this is because people behave less rationally when ideas are at stake than when money is at stake. However, it has become an important tool for clarifying the underlying logic of a number of more paradigmatic problems.

In biology, game theory has been widely used to understand and predict certain outcomes of evolution, such as the concept of stable evolutionary strategy introduced by John Maynard Smith in his essay "Game Theory and the Evolution of Fighting" Evolution of La Lucha ”, as well as in his book“ Evolution and Game Theory ”.

Regarding philosophy, game theory can show that even the most selfish individuals may find that sometimes cooperating with others can be in their own best interests.

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