| From your link, >The prisoner's dilemma is a canonical example of a game analyzed in game theory that shows why two purely "rational" individuals might not cooperate, The generalized prisoner's dilemma is indeed well-known; the name "prisoner's dilemma", without further qualification, does, however, refer to the case of two perfectly rational players (hence the title of the wiki article you linked). In either case, the generalized prisoner's dilemma generalizes the payoffs and penalties, but still assumes two players. Perhaps you were thinking of the iterated prisoner's dilemma since it does deal with more than two players; however, the iterated prisoner's dilemma deals with playing the game more than once in succession, while here we have a single round with an unknown number of players. As it stands, the given problem is not a version of the prisoner's dilemma, but an entirely different sort of problem altogether. We could perhaps impose additional constraints in order to reduce it to some generalization of the prisoner's dilemma; in any case, as stated, we cannot say that this is "the prisoner's dilemma with extra credit" in any meaningful sense. (significantly edited for clarity and organization) Further edit: I am not aware of a canonical statement and solution of an N-player prisoner's dilemma. I would be interested in a reference. |
I was not confusing iterated and n-player versions.
For a ref, eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.... and it gives some further citations.