What is Game Theory?

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  • Topic: Game theory, John von Neumann, Nash equilibrium
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What is Game Theory?

Game theory is a branch of mathematics that aims to lay out in some way the outcomes of strategic situations. Game theory has applications in politics, inter-personal relationships, biology, philosophy, artificial intelligence, economics, business and other disciplines. Originally, game theory attempted to look only at a fairly limited set of circumstances, those known as zero sum games, but in recent years its scope has increased greatly.

Brief history

John von Neumann is looked at as the father of modern game theory, largely for the work he laid out in his seminal 1944 book, Theory of Games and Economic Behavior, but many other theorists, such as John Nash and John Maynard Smith, has advanced the discipline.

Since game theory became established as a discipline in the 1940s, and since it became even more embedded in mathematics and economics through John Nash’s work in the 1950s, a number of practitioners of game theory have won Nobel Prizes in Economics.

Game Theory's Most Important Minds

John von Neumann, whose 1944 book Theory of Games and Economic Behavior, written with Oscar Morgenstern, made him arguably the founding father of modern game theory

John Nash, whose story was told in the film A Beautiful Mind and whose achievements have helped make him one of the best-known game theorists

Kenneth Arrow, whose famous "impossibility theory" proved that designing a fundamentally unflawed voting system is essentially impossible

Barry Nalebuff and Adam Brandenberger, whose 1996 book on Co-Competition offered modern business an innovative rethinking of the competitiveness.

How does it work?

Game theory basically works by taking a complex situation in which people or other systems interact in a strategic context. It then reduces that complex situation to its most basic "game," allowing it to be analyzed and for outcomes to be predicted. As a result, game theory allows for prediction of actions that otherwise could be extremely difficult, and sometimes counter intuitive, to understand.

Examples of ‘Games’ to describe Game Theory

Theorists have used several ‘games’ to describe this theory. Some of them are Cake Cutting game, the Stag Hunt, the Dollar Auction, the Coordinators Game, the Dictator Game, and the Ultimatum Game. Games are generally separated into two categories, depending on whether they are zero-sum, meaning the gains gained by one player or group of players are equaled by the losses by others, or non-zero-sum.

One way to describe a game is by listing the players (or individuals) participating in the game, and for each player, listing the alternative choices (called actions or strategies) available to that player. In the case of a two-player game, the actions of the first player form the rows and the actions of the second player the columns, of a matrix. The entries in the matrix are two numbers representing the utility or payoff to the first and second player respectively.

The famous ‘Prisoner's Dilemma’

A very famous game is the Prisoner's Dilemma game. In this game the two players are partners in a crime who have been captured by the police. Each suspect is placed in a separate cell, and offered the opportunity to confess to the crime. The game can be represented by the following matrix of payoffs-

Not confessconfess

Not confess5, 5-4, 10

Confess10,-41, 1

Note that higher numbers are better (more utility). If neither suspect confesses, they go free, and split the proceeds of their crime which we represent by 5 units of utility for each suspect. However, if one prisoner confesses and the other does not, the prisoner who confesses testifies against the other in exchange for going free and gets the entire 10 units of utility, while the prisoner who did not confess goes to prison and which results in the low utility of -4. If both prisoners confess, then both are given a reduced term, but both are convicted, which we...
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