The genericity of beliefs-determine-preferences models revisited

Barelli [P. Barelli, On the genericity of full surplus extraction in mechanism design, J. Econ. Theory 144 (2009) 1320-1332] defines beliefs-determine-preferences (BDP) models and argues that BDP models are nongeneric in a topological sense. In this note, we point out some difficulties in Barelli[modifier letter apostrophe]s approach. Furthermore, we follow the idea of Heifetz and Neeman [A. Heifetz, Z. Neeman, On the generic (im)possibility of full surplus extraction, Econometrica 74 (2006) 213-233] to propose a more relevant notion of BDP* model. We prove that BDP* models are generic, which is opposite to Barelli[modifier letter apostrophe]s conclusion.