LectureFeb22_MATH4321_12S

LectureFeb22_MATH4321_12S - Remark: In the above analysis,...

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Remark: In the above analysis, we used the basic assumption of Common Knowledge. A fact is common knowledge if everyone knows it, everyone knows that everyone knows it, everyone knows that everyone knows that everyone knows it,. .., and so on ad infinitum. 你知 , 我知 , 你知我知 , 我知你知 , ……. .
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Common knowledge is a phenomenon which underwrites much of social life. In order to communicate or otherwise coordinate their behavior successfully, individuals typically require mutual or common understandings or background knowledge. If a married couple are separated in a department store, they stand a good chance of finding one another because their common knowledge of each others' tastes and experiences leads them each to look for the other in a part of the store both know that both would tend to frequent. Since the spouses both love cappuccino, each expects the other to go to the coffee bar, and they find one another. In A Treatise of Human Nature , Hume argued that a necessary condition for coordinated activity was that agents all know what behavior to expect from one another. Without the requisite mutual knowledge, Hume maintained, mutually beneficial social conventions would disappear.
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Princess Bride (Revie(w by Mike Shor) http://www.youtube.com/watch?v=U_eZmEiyTo0 Our hero Westley, in the guise of the Dread Pirate Roberts, confronts his foe-for-the-moment, the Sicilian, Vizzini. Westley challenges him to a Battle of Wits. Two glasses are placed on the table, each containing wine and one purportedly containing poison. The challenge, simply, is to select the glass that does not lead to immediate death. Roberts: All right: where is the poison? The battle of wits has begun. It ends when you decide and we both drink, and find out who is right and who is dead. Vizzini: But it's so simple. All I have to do is divine from what I know of you. Are you the sort of man who would put the poison into his own goblet, or his enemy's? Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I'm not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me.
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Vizzini: Not remotely. Because iocane comes from Australia, as everyone knows. And Australia is entirely peopled with criminals. And criminals are used to having people not trust them, as you are not trusted by me. So I can clearly not choose the wine in front of you. Roberts: Truly, you have a dizzying intellect. The scene, beyond providing some comic relief on the theme of common knowledge, also has an important lesson on strategic moves; if the rules of the game may be changed, then the game can be rigged to one player's advantage: Vizzini: let's drink -- me from my glass, and you from yours. [allowing Roberts to drink first, he swallows his wine]
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This note was uploaded on 03/13/2012 for the course MATH 4321 taught by Professor Cheng during the Spring '12 term at HKUST.

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LectureFeb22_MATH4321_12S - Remark: In the above analysis,...

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