# Game theory

(Redirected from Non-zero sum game)
 Part of the series on 2+2=4 v - t - e

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.

In game theory, a particular model is referred to as a "game." 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 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(ies). 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 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).

Some politicians treat the economy as though it were a static zero sum game, with rhetoric about how the "rich get richer and the poor get poorer".[1] This would only be true in the extremely rare case of zero GDP growth. President Bush explained all of this when he said we ought to work harder to put food on our families and make the pie higher.

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 its 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.

### 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 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, information exchange/communication

### 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 prisoner's 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 bulk of the punishment, while Prisoner B will be punished less severely. Or, both Prisoner A and Prisoner B can spill their guts, both get punished, but not as severely. But, if both keep their mouths shut, the police will not be able to convict either, forcing both to be released.

The set up is simple enough, and the obvious thing to do is to not talk, and hope your partner doesn't talk. The situation created is one where, due to incomplete information, both parties will tend to (paradoxically) move towards a situation where both parties lose.

## Footnotes

1. Leonard Cohen, "Everybody Knows"