How People Interact and Make Decisions

Game Theory

Summary of Game Theory. Abstract

John von Neumann

Oskar Morgenstern

John Nash

Game Theory (GT) is a special branch of mathematics which has been developed to study decision making in complex circumstances. The idea to see business as a game, in the sense that a move by one player sparks of moves by others, runs through modern strategic thinking. It historically dates back to the Talmud and Sun Tzu's writings. However, its contemporary codification is credited to John von Neumann and Oskar Morgenstern who, in 1944, published Theory of Games and Economic Behavior. In the early 1950s, John Nash generalized these results and provided the basis of the modern field. A rapid rise in theoretical developments led to the founding of the first academic journal devoted to the field by Oskar Morgenstern in 1972. Few corporations nowadays think about their strategy without adding some GT models or game elements into their strategy process.

GT can be defined as the study of how people interact and make decisions. This broad definition applies to most of the social sciences, but GT applies mathematical models to this interaction under the assumption that each person's behavior impacts the well-being of all other participants in the game. These models are often quite simplified abstractions of real-world interactions. While many game theorists certainly enjoy playing games, a "game" is an abstract representation of many serious situations and has a serious purpose.

A major issue with game theory is that is is necessary to make assumptions. Any model of the real world must make simplifying assumptions because the real world is too messy to analyze with any precision. There is a constant tradeoff between realism and solvability. Even if one could write down a model that accurately describes how people make decisions in general, no amount of computers would be able to calculate it.

What assumptions are made normally? The most common ones are:

- rationality (people take whatever actions are likely to make them more happy - and they know what makes them happy), and

- common knowledge (we know that everyone else is trying to make himself or herself as happy as possible, potentially at our expense).

These assumptions take many mathematical forms, from very strong (and likely unrealistic) to much weaker forms in the study of behavioral GT.

Experimental economics examines the validity of these assumptions by seeing how real people act in controlled environments.

The most widely known example of game theory is probably the prisoner's dilemma: A zero-sum game cooperation game that got its name from the following hypothetical situation: imagine two criminals arrested under the suspicion of having committed a crime together. However, the police does not have sufficient proof in order to have them convicted. The two prisoners are isolated from each other, and the police visit each of them and offer a deal: the one who offers evidence against the other one will be freed. If none of them accepts the offer, they are in fact cooperating against the police, and both of them will get only a small punishment because of lack of proof. They both gain. However, if one of them betrays the other one, by confessing to the police, the defector will gain more, since he is freed; the one who remained silent, on the other hand, will receive the full punishment, since he did not help the police, and there is sufficient proof. If both betray, both will be punished, but less severely than if they had refused to talk. The dilemma resides in the fact that each prisoner has a choice between only two options, but cannot make a good decision without knowing what the other one will do.

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