Rationality Versus Common Knowledge of Rationality
This game illustrates the difference between perfect rationality of an actor and the common knowledge of rationality of all players. Even perfectly rational players playing in such a game should not guess 0 unless they know that the other players are rational as well and that all players' rationality is common knowledge. If a rational player reasonably believes that other players will not follow the chain of elimination described above, it would be rational for him/her to guess a number above 0.
Interestingly, we can suppose that all the players are rational, but they do not have common knowledge of each other's rationality. Even in this case, it is not required that every player guess 0, since they may expect each other to behave irrationally.
Read more about this topic: Guess 2/3 Of The Average
Famous quotes containing the words common and/or knowledge:
“All the philosophy, therefore, in the world, and all the religion, which is nothing but a species of philosophy, will never be able to carry us beyond the usual course of experience, or give us measures of conduct and behaviour different from those which are furnished by reflections on common life. No new fact can ever be inferred from the religious hypothesis; no event foreseen or foretold; no reward or punishment expected or dreaded, beyond what is already known by practice and observation.”
—David Hume (1711–1776)
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—John L. Balderston (1899–1954)