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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.
See also Dilemma, Tit-for-Tat
References
Axelrod, R. The Evolution of Cooperation New York: BasicBooks, 1985.
Goetz, P. ``Phil's Good Enough Complexity Dictionary.''
http://www.cs.buffalo.edu/~goetz/dict.html.