# Game theory

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Not to be confused with Game Theory, a YouTube show by MatPat that's known for gaming-related videos.
 “”Only two groups in society actually behave in a rational, self-interested way in all experimental situations. One is economists themselves, the other is psychopaths. —Adam Curtis, The Trap: The Lonely Robot

Game theory is a way of modelling complex phenomena in simple, mathematical ways, showing gains and losses in the form of "points". It is used most often in psychology, sociology, economics, and international relations, to model how people act with each other, though biologists also sometimes use it to describe how non-human organisms[note 1] interact with each other.

In game theory, a particular model is referred to as a "game".[1][note 2][note 3] The most famous game is that of the prisoner's dilemma. However, there are as many games as there are possible situations to diagram.

In international relations, it is now most used by neoliberal institutionalists to model how states may engage in trade or other forms of cooperation, and how to induce "side payments" to reduce the inequity in the gains. Previously, it was mostly used by deterrence theorists to describe how to threaten others to convincingly engage in deterrence.

## Risks

See the main article on this topic: Risk

A risk is a situation where the outcome is unknown, while carrying some chance of loss and/or injury.

In many of life's situations, the only possibilities of gain include some risk, such as investing in a business or trusting another person. "Risk management" is the art and science of minimizing the risk inherent in a given endeavor. Colloquially, "risky behavior" means activities that are perceived as having a very high risk to benefit ratio, especially if the risks can easily be reduced by simple means.

Parts of game theory study the risk versus reward aspect of artificial and real life situations.

## Some common games

There are really hundreds of games in game theory, but the following are some of the most commonly referenced, and are common in introductory courses.

### Zero-sum game

A zero-sum game is a situation, according to game theory, where for one person (or side) to win, another must lose — i.e. that any advantage accrued by one party to the negotiations must be obtained at the expense of the other party or parties. Essentially: in the whole group of players, there is nothing to be gained or lost, only things to move from one player to another.

Many card and board games are zero-sum games, in that only one can win, and in that there are a fixed amount of winnings to be had.

Contrast this relatively artificial situation with the many real-life situations that are non-zero-sum games (see below).

One of the biggest disagreements between liberals and realists in international relations has to do with the nature of the international economy, and whether or not it's a zero-sum game. Liberals maintain that cooperation can make everyone better off, and so it's not a zero-sum game. Realists insist that what matters isn't the absolute gains a state can make, but instead how well-off it is compared to other states. This would then, indeed, be a zero-sum game. Probably the truth lies in-between.

### Non-zero-sum game

A non-zero-sum game is a concept in game theory in which the aggregate gains and losses between the parties involved can be greater than or less than zero. Essentially, it means that one person receiving gains does not mean that the others in the game must lose, and that losses do not necessarily translate into gains for other players. This is contrasted with zero-sum games where each loss or gain is associated with a corresponding loss or gain to other players, so that that aggregate total always sums to zero. Essentially, in the whole system, it is possible to increase or decrease the total amount of points.

Non-zero-sum games have been used to describe many important relationships both in psychology and economics. There are many famous games developed by researchers that tap into fundamental relationships between people. One of the most widely used and cited is the prisoner's dilemma game that has been used to describe many areas of human social interaction, from advertising to nuclear warfare.

Non-zero-sum game is used in the stock market, international trade, investment, reciprocal altruism, and information exchange/communication, among other applications.

### Prisoner's dilemma

See the main article on this topic: Prisoner's dilemma

The prisoner's dilemma is a situation where two people who committed a crime are being interrogated in separate rooms, giving them two choices on how to act, creating three possible outcomes. We'll call the prisoners Prisoner A and Prisoner B.

• If Prisoner A keeps his mouth shut and doesn't say anything, but Prisoner B spills his guts, Prisoner A will get the worst punishment, while Prisoner B will walk free.
• Symmetrically, if Prisoner A speaks up but Prisoner B stays silent, Prisoner A walks free and B is severely punished.
• If both Prisoner A and Prisoner B confess, both get punished, but to a lesser degree.
• Lastly, if both keep their mouths shut, the police will not be able to convict either, forcing both to receive the least punishment for a different, unrelated crime.

The set-up is simple enough. The best result (from the prisoners' perspective) would be for both to stay silent and get off easy. Paradoxically, from the individual perspective, confessing is always the better option (if the other one stays silent, you walk free; if he blabs, you at least don't get the worst punishment). Things can get more complicated based on other factors, such as how much information each prisoner has about the decision the other is likely to make.