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:
“The propensity to truck, barter and exchange one thing for another ... is common to all men, and to be found in no other race of animals.”
—Adam Smith (1723–1790)
“A man can only attain knowledge with the help of those who possess it. This must be understood from the very beginning. One must learn from him who knows.”
—George Gurdjieff (c. 1877–1949)