# Game Theory

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## Studying through applying mathematical models how people interact and make decisions. Explanation of Game Theory of Von Neumann, Morgenstern, and Nash.

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### What is Game Theory? Description

Game Theory is a special branch of mathematics which has been developed for studying decision-making in complex circumstances. Game theory tries to predict outcomes based on interactive models in which the decisions of each party affect the decisions of the other parties. The meaning of "Game" here is: a move by one player will result in moves by others. The idea historically dates back to the Talmud and Sun Tzu's writings. However, the contemporary codification is attributed to John von Neumann and Oskar Morgenstern. They published the Theory of Games and Economic Behavior in 1944. In the early 1950s, John Nash generalized their results and provided the basis of the modern field of Game Theory. A rapid rise in theoretical developments led to the founding of the first academic magazine devoted to the field by Oskar Morgenstern in 1972. Few corporations nowadays think about their strategy without adding some game theory models or game elements into their strategy process.

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. Applications

• 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.

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