What Keynes called the Newspaper Beauty Contest is known to modern game theory as a variant of the Common Knowledge game. To illustrate how this game is played on a fundamental level, I’ll use another classic example: The Island of the Green-Eyed Tribe.On the Island of the Green-Eyed Tribe, blue eyes are taboo. If you have blue eyes, you must get in your canoe and leave the island at dawn the morning after you learn the truth. But there are no mirrors or reflective surfaces on the island, so no one has actually ever seen the colour of his or her own eyes. It is also taboo to talk or otherwise communicate with each other about eye colour, so if anyone saw that you had blue eyes, he wouldn’t tell you. Similarly, when you see a fellow tribe member with blue eyes, you are not allowed to tell him or her the true state of his eye colour. Every tribe member knows the eye colour of everyone else, but not his or her own eye colour.A missionary announces to everyone that at least one of them ...
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