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:
“For Banquo’s issue have I filed my mind;
For them the gracious Duncan have I murdered;
Put rancors in the vessel of my peace
Only for them; and mine eternal jewel
Given to the common enemy of man,
To make them kings, the seeds of Banquo kings!”
—William Shakespeare (1564–1616)
“The new knowledge has not yet settled in culture. It has not yet been integrated in a new cosmic conception.”
—Johan Huizinga (1872–1945)