Beliefs, payoffs, information: On the robustness of the BDP property in models with endogenous beliefs

Neeman (2004) and Heifetz and Neeman (2006) have shown that, in auctions with incomplete information about payoffs, full surplus extraction is only possible if agents’ beliefs about other agents are fully informative about their own payoff parameters. They argue that the set of incomplete-information models with common priors that satisfy this so-called BDP property (“beliefs determine preferences”) is negligible. In contrast, we show that, in models with finite-dimensional abstract type spaces, the set of belief functions with this property is topologically generic in the set of all belief functions. Our result implies genericity of (non-common or common) priors with the BDP property.