Game Theory is a study of strategic decision making. More formally, it is “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.” An alternative term suggested “as a more descriptive name for the discipline” is interactive decision theory. Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person’s gains exactly equal net losses of the other participant(s). Today, however, game theory applies to a wide range of behavioral relations, and has developed into an umbrella term for the logical side of decision science, to include both human and non-humans, like computers.

Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann’s original proof used Brouwer’s fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was followed by his 1944 book Theory of Games and Economic Behavior, with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.

Game theory can be defined as the study of how people interact and make decisions. This broad definition applies to most of the social sciences, but game theory 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.

### Usage of Game Theory

- Preparing business negotiations.
- Analyzing future market conditions.
- Strategic decision-making.
- Assess the viability of a new venture, business model, program, project, product, service or technology.

### Assumptions in Game Theory

A major issue with game theory is: it is necessary to make assumptions. Any model of the real world must make assumptions that simplify the reality, because the real world is too complex to analyze with any precision. There is a constant tradeoff between realism and the technical capability to solve problems. 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 usual assumptions are:

- Rationality. People take whatever actions are likely to make them more happy. And they know what makes them happy.
- Common knowledge. We know that everyone is trying to make himself as happy as possible, potentially at our expense.

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

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

### Example of Game Theory

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 to have them convicted. The two prisoners are being isolated from each other, and the police offers each of them a deal: the person that 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 will both win. However, if one person betrays the other, by confessing to the police, he 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 they can not make a good decision, without knowing what the other person will do.