If valuations are interdependent and agents observe their own allocation payoffs, then two-stage revelation mechanisms expand the set of implementable decision functions. In a two-stage revelation mechanism agents report twice. In the first stage - before the allocation is decided - they report their private signals. In the second stage - after the allocation has been made, but before final transfers are decided - they report their payoffs from the allocation. Conditions are provided under which an uninformed seller can extract (or virtually extract) the full surplus from a sale to privately informed buyers, in spite of the buyers’ signals being independent random variables
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