CeDEx workshop - Alia Gizatulina (Max Planck Institute for Research on Collective Goods, Bonn)

Betting on Others’ Bets

We construct the generalized Crémer-McLean mechanism where i’s participation fee depends not only on the valuations reported by -i at the second stage, but also on the choice of the participation fee by -i at the first stage. Such construction allows to exploit the convex hull property of beliefs whenever it appears in beliefs about beliefs rather than in beliefs about preferences. As such betting retrieves agents’ entire hierarchies of beliefs, it reveals what is common knowledge among them. Hence, in an environment where the designer is uncertain about agents' type space and perceives as possible a finite or countable collection of type spaces, each verifying the convex hull property, he can propose a union of GCM mechanisms and so extract surplus across type spaces, i.e., regardless of absence of knowledge by the designer which type space agents share (and without relying on the shoot-the-liar mechanism).