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3. Ex-ante, this the weakest form. Assuming every player have no knowledge for neither others and itself, the player decide to participate based on the prior distribution of the players type (and then calculate its expected utility).
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2. Interim, this is in the middle. Assuming every player only knows its own type, it decides to participate the game given that its expected utility is greater than its outside option.
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Unfortunately, it can frequently be shown that participation constraints are incompatible with other desirable properties of mechanisms for many purposes. One of the classic result is
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are said to be satisfied if a mechanism leaves all participants at least as well-off as they would have been if they hadn't participated.
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In terms of information structure, there are 3 types of
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