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Game theory is a branch of mathematics that analyzes strategic situations and has applications in various fields. It reduces complex situations to basic “games” to predict outcomes. The prisoner’s dilemma is a popular example, where confessing is the smartest decision. Other games include Cake Cutting, Stag Hunt, and Ultimatum Game. Games are divided into zero-sum and non-zero sum categories.
Game theory is a branch of mathematics that aims to somehow define the outcomes of strategic situations. It has applications in politics, interpersonal relationships, biology, philosophy, artificial intelligence, economics, and other disciplines. Originally, it attempted to examine only a fairly limited set of circumstances, those known as zero-sum games, but its scope has increased significantly in recent years. John von Neumann is considered the father of modern game theory, largely for the work he presented in his seminal 1944 book, Theory of Games and Economic Behaviour, but many other theorists, such as John Nash and John Maynard Smith, have advanced the discipline.
Since game theory established itself as a discipline in the 1940s, and since it became even more entrenched in mathematics and economics through the work of John Nash in the 1950s, a number of game theory practitioners have won Nobel prizes for economics.
Game theory basically works by taking a complex situation where people or other systems interact in a strategic context. It then reduces that complex situation to its most basic “game”, allowing for its analysis and prediction of outcomes. As a result, it allows you to predict actions that might otherwise be extremely difficult and sometimes counter-intuitive to understand. A simple game that most people are very familiar with is Rock, Paper, Scissors, which is used by some game theorists, although due to its lack of information it doesn’t have much relevance in real world situations.
One of the most prominent examples of a widely known game is referred to as the prisoner’s dilemma. In this scenario, let’s imagine two criminals caught by the police after committing a crime, such as robbing a bank of 10 million US dollars (USD) together. They are each placed in separate rooms and the police ask them to confess. If one prisoner confesses and the other does not, the confessor is left free to keep the $10 million for himself, while the other goes to prison for four years. If neither confesses, they will both be released for lack of evidence and will each withhold $5 million dollars. If both confess, their sentences are reduced for cooperating, but both still spend a year in prison.
The prisoner’s dilemma is important in game theory for a variety of reasons and is expanded to cover much more complex situations. The smartest decision to make in the situation given in the prisoner’s dilemma is to confess no matter what. It minimizes the personal risk and outweighs the personal gain of both being set free. As with many games in game theory, this simple game can be extended to many different situations in the real world with similar circumstances: an easy example is two companies competing in the market, where it is in both sides’ interests to set high prices, but even better to set a low price while the competitor sets a high price.
Other popular game theory games include Cake Cutting Game, Stag Hunt, Dollar Auction, Coordinators Game, Dictator Game and Ultimatum Game. Games are generally divided into two categories, depending on whether they are zero-sum, meaning that the gains made by one player or group of players are equal to the losses of the others, or non-zero sum.
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