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 satisfying this so-called BDP property (beliefs determine preferences) is negligible, in a geometric and a measure-theoretic sense. In contrast, we show that, in models with finite-dimensional type spaces, this property is topologically generic if the set of objects about which beliefs are formed is sufficiently rich and beliefs are derived by conditioning on the available information; for any agent, this information includes his own payoff parameters.