What is Game Theory?

Brendan McGuigan

Game theory is a branch of mathematics that aims to lay out in some way the outcomes of strategic situations. It has applications in politics, inter-personal relationships, biology, philosophy, artificial intelligence, economics, and other disciplines. Originally, it 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. 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, have 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 this subject have won Nobel Prizes in Economics.

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, it allows for prediction of actions that otherwise could be extremely difficult, and sometimes counter intuitive, to understand. One simple game most people are very familiar with is Rock, Paper, Scissors, which is used by some game theorists, although because of its lack of information it does not have a great deal of relevance on real world situations.

One of the most important examples of a widely-known game is referred to as the Prisoner’s Dilemma. In this scenario, we imagine two criminals captured 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 for them to confess. If one prisoner confesses, while the other doesn’t, the confessor is let off free to keep the \$10 million USD for themselves, while the other will go to jail for four years. If neither confess, they will both be let off for lack of evidence, and will each keep \$5 million USD. If both confess, their sentences are reduced for cooperating, but they still both spend a year in jail.

The Prisoner’s Dilemma is important in game theory for a number of reasons, and is expanded on to arrive at much more complex situations. The most intelligent decision to make in the situation given in the Prisoner’s Dilemma is to confess, no matter what. It minimizes personal risk, and outweighs the personal gain of both being let off free. As with many games in game theory, this simple game can be expanded to many different situations in the real world with similar circumstances: an easy example is two businesses competing in the market, where it is in both parties’ best interest to set high prices, but even better to set a low price while the competitor sets a high price.

Other famous game theory games include the 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.

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arod2b42

@GigaGold

Do you really think people can be put into stereotypes or "categorical roles" that easily? I believe that there is more to people than simply functionality that is chartable by logic and mathematics. John Nash seems to have missed this fact.

GigaGold

@BostonIrish

Many other fields have employed game theory in maximizing their effect. Part of Operations Management is researching leadership patterns of managers and determining the best suitable job and efficiency for them and their respective employees. Game theory comes into play when the psychology of a group is taken into account and requires some intuition in regards to where a person's skills will work best.

BostonIrish

In more advanced game theory, people fit into certain categorical roles which determine what their actions are most likely to be. Depending on someone's historical tendencies, based on psychological patterns, environmental conditioning, childhood experience, etc., they may be more inclined to take an aggressive or random stance in certain game contexts than others, and therefore can be expected to work certain ways. "Understanding your opponent" becomes an important factor when seeking to use game theory to ones best advantage.