'I Don't Want to Know !': Can It Be Rational?

Bruno Bassan, Marco Scarsini & Shmuel Zamir

In this paper we will show that the usually accepted principle of decision theory that the "the more information the better" seemingly breaks down in stategic contexts. We will show through several examples that almost every situation is conceivable: Information can be beneficial for all the players, or only for the one who receives it,or, less intuitively, just for the one who does not receive it, or it could be bad for both. The only class of games that escapes these seemingly surprising phenomena is the class of zero-sum games, but only under the assumption of common beliefs for the players. We will show that even aminor departure from the assumptions of zero-sum and common beliefs can produce the phenomenon of information-rejection. We will show that these phenomena may appear even in coordination games, where one would expect that public information should facilitate coordination. It should be emphasized that there is here neither a pathology nor a paradox: aside from the particular examples that may merit attention, the message is that in an interactive decision framework with incomplete information, the relevant issue is that of interactive knowledge rather than simply knowledge per se.

November, 1997
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