Informational smallness and the scope for limiting information rents

For an incomplete-information model of public-good provision with interim participation constraints, we show that efficient outcomes can be approximated, with approximately full surplus extraction, when there are many agents and each agent is informationally small. The result holds even if agents' payoffs cannot be unambiguously inferred from their beliefs, i.e., even if the so-called BDP property (Beliefs Determine Preferences) of Neeman (2004) does not hold. The contrary result of Neeman (2004) rests on an implicit uniformity requirement that is incompatible with the notion that agents are informationally small because there are many other agents who have information about them.