Informational smallness and the scope for limiting information rents

Abstract

For an incomplete-information model of public-good provision with interim participation constraints, we show that e¢ cient 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' payo¤s 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.JEL Classi…cation: D40, D44, D80, D82

Robust Mechanism Design

“…Other results in the literature can be understood as reflecting intermediate classes of type spaces in between payoff type spaces and the universal type space. Gizatulina and Hellwig (2010) consider all type spaces with the restriction that agents are informationally small in the sense of McLean and Postlewaite 2002; they show that notwithstanding a failure of the BDP property highlighted by Neeman (2004), it is possible to extract almost the full surplus in quasilinear environments. We follow Ledyard (1979) in restricting attention to full support type spaces in Chapter 1 (Section 4.2).…”

“…Bergemann and Morris (2001) noted that among the (infinite) space of all finite common prior types within the universal type space, one can always perturb a BDP type by a small amount in the product topology and get a non-BDP type and conversely perturb the non-BDP type by a small amount to get back to a BDP type. For topological notions of genericity, answers depend on the topology adopted and the topological definition of genericity employed (see results in Dekel, Fudenberg, and Morris (2006), Barelli (2009), Chen and Xiong (2010), Chen and Xiong (2011) and Gizatulina and Hellwig (2011)). 5 Heifetz and Neeman (2006) report an approach based on alternative geometric and generalized measure theoretic views of genericity for infinite state spaces.…”