The generic possibility of full surplus extraction in models with large type spaces - Alia Gizatulina; Martin Hellwig (Max Planck Institute for Research on Collective Goods, 2017)
McAfee and Reny (1992) have given a necessary and sufficient condition for full surplus extraction in naive type spaces with a continuum of payoff types. We generalize their characterization to arbitrary abstract type spaces and to the universal type space and show that in each setting, full surplus extraction is generically possible. We interpret the McAfee-Reny condition as a much stronger version of injectiveness of belief functions and prove genericity by arguments similar to those used to prove the classical embedding theorem for continuous functions. Our results can be used to also establish the genericity of common priors that admit full surplus extraction.
Keywords: D40; D44; D80; D82; 330; mechanism design; surplus extraction; abstract type spaces; universal type space; genericity; correlated values; correlated information; strategic continuity