Game theory

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Game theory is the study of how and why people make decisions.[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]

In the Cold War period, the strategic decisions of the United States and the Soviet Union were sometimes viewed as an exercise in game theory.[6] In that case the "players" being studied were the United States and the Soviet Union.[7][8]

Game theory is not just about games, but how and why businesses make decisions, and just about any decision based on valuing likely outcomes.[9] In game theory, all of these situations are "games" since the people involved make choices based on how they value the possible outcomes of the choices. This is true even of cases where the decisions of a single person only affect that one person.

Game theory is found in the financial choices people make, and is found in the study of economics.[10]

Prisoner's Dilemma[change | change source]

One example is the prisoner's dilemma.[2] It gives an example where co-operation may not be the "best choice" in game theory.

Suppose two people are arrested for a crime, and the police are uncertain which person committed the crime, and which person abetted the crime. Each is given a choice: If each remains silent, they are both soon released. If one betrays the other, the betrayer goes free, and the other is imprisoned for a long time. If each betrays the other, they both are held for a shorter time.

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 short, "betrayal" is the best strategy, and is called the "dominant strategy."

Variations[change | change source]

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[change | change source]

  1. Williams J.D. 1954. The compleat strategyst: being a primer in the theory of games of strategy. New York: McGraw-Hill.
  2. 2.0 2.1 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. ISBN 0-472-08741-X
  10. McNulty, Daniel. "The basics of game theory". Retrieved 2015-02-28.