# Game theory

Game theory studies decision-making strategy.[1][2][3] Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".[4] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory.[5]

Game theory was prominent in the Cold War period, as experts tried to get to grips with the ideas of nuclear deterrence and bargaining.[6] In that case the "players" being studied were the United States and the Soviet Union.[7][8]

So, game theory studies more than just board games, sports, and games of luck.[9] It also studies things like business and military decisions. In game theory, people call all of these situations "games." In other words, you can use game theory to study any situation where more than one person makes choices.

The players in a game are not even always people. Players can be people, companies, armies, dogs or other things. Each player wants something: maybe a company wants to make as much money as it can, or a country wants to win a war. Sometimes the players work together, but often they are competing against each other.

Game theory is also part of economics.[10]

## Prisoner's Dilemma

One important game is the prisoner's dilemma.[2] It's an imaginary situation that shows why sometimes people do not cooperate (help each other).

### Setup

Imagine this situation: the police catch two criminals after they committed a crime. The police do not know which person committed the crime and which person just helped. They question the two in separate cells. Each prisoner can either stay silent or betray (hurt) the other by blaming the crime on them. If both stay silent, they only go to jail for 6 months. If one betrays and the other stays silent, the one that stays silent goes to jail for 10 years and the other one does not go to jail at all. If they both betray each other, they each go to jail for 2 years. No matter what happens, the prisoners will never see each other again.

### Strategies

If you are a prisoner in this situation and you only care about yourself, the way to get the smallest sentence is to betray the other prisoner. No matter what, you get a shorter sentence when you betray than when you do not. If the other prisoner stays silent and does not betray, then betraying means you do not go to jail at all instead of going to jail for 6 months. If the other prisoner betrays, then betraying lets you go to jail for 2 years instead of 10 years. In other words, it's always best for you to betray, even though the two of you would be better off if you both stayed silent. It is said that betraying the other prisoner is your "dominant strategy" because it is always the best thing for you to do, no matter what the other prisoner does.

The prisoner's dilemma is like a lot of other situations in the real world. For example, if two countries are trying to decide whether to make new weapons, they are both better off if neither country does. But sometimes the countries are in the same situation as the prisoners: each country only cares about itself, and it's better off if it "betrays" the other country by making weapons.

### Variations

The prisoner's dilemma does not have same result if some of the details are different. If the prisoners (or countries) can talk with each other and plan for the future, they might both decide to cooperate (not betray) because they hope that will make the other country help them in the future. In game theory, this is called a "repeated game." If the players are altruistic (if they care about each other), they might be okay with going to jail so they can help the other person.

## References

1. Williams J.D. 1954. The compleat strategyst: being a primer in the theory of games of strategy. New York: McGraw-Hill.
2. Rapoport A. & Chammah A.M. 1965. Prisoner's dilemma: a study in conflict and cooperation. Ann Arbor: University of Michigan Press.
3. Rapoport, Anatol 1966. Two-person game theory: the essential ideas. Ann Arbor: University of Michigan Press. ISBN 0-472-05015-X
4. Myerson R.B. (1991). Game theory: analysis of conflict, Harvard University Press, p. 1. Chapter-preview links, pp. vii–xi.
5. Aumann R.J. [1987] 2009. The New Palgrave: a dictionary of economics. "Game theory", Introduction, 2nd ed. Abstract.
6. Stone J.J. 1967. Strategic persuasion: arms limitations through dialogue. New York: Columbia University Press.
7. Kahn H. 1960. On thermonuclear war. Princeton University Press. ISBN 0-313-20060-2
8. Kahn H. 1962. Thinking about the unthinkable. Horizon Press.
9. Rapoport A. 1960. Fights. games and debates. Ann Arbor: University of Michigan Press. IBSN 0-472-08741-X
10. McNulty, Daniel. "The basics of game theory". Retrieved 2015-02-28.