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# Prisoner's Dilemma

A problem in game theory first discussed by A. Tucker. Suppose each of two prisoners and , who are not allowed to communicate with each other, is offered to be set free if he implicates the other. If neither implicates the other, both will receive the usual sentence. However, if the prisoners implicate each other, then both are presumed guilty and granted harsh sentences.

A dilemma arises in deciding the best course of action in the absence of knowledge of the other prisoner's decision. Each prisoner's best strategy would appear to be to turn the other in (since if makes the worst-case assumption that will turn him in, then will walk free and will be stuck in jail if he remains silent). However, if the prisoners turn each other in, they obtain the worst possible outcome for both.

Mosteller (1987) describes a different problem he terms "the prisoner's dilemma." In this problem, three prisoners , , and with apparently equally good records have applied for parole, and the parole board has decided to release two, but not all three. A warder knows which two are to be released, and one of the prisoners () asks the warder for the name of the one prisoner other than himself who is to be released. While his chances of being released before asking are 2/3, he thinks his chances after asking and being told " will be released" are reduced to 1/2, since now either and or and are to be released. However, he is mistaken since his chances remain 2/3.

The Season 1 episode "Dirty Bomb" (2005) of the television crime drama NUMB3RS mentions the Prisoner's dilemma.

Dilemma, Monty Hall Problem, Tit-for-Tat

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## References

Axelrod, R. The Evolution of Cooperation. New York: BasicBooks, 1985.Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 164-165, 1998.Goetz, P. "Phil Goetz's Complexity Dictionary." http://www.cs.buffalo.edu/~goetz/dict.htmlMosteller, F. "The Prisoner's Dilemma." Problem 13 in Fifty Challenging Problems in Probability with Solutions. New York: Dover, pp. 4 and 14-15, 1987.

## Referenced on Wolfram|Alpha

Prisoner's Dilemma

## Cite this as:

Weisstein, Eric W. "Prisoner's Dilemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrisonersDilemma.html