Robust virtual implementation with almost complete information

Abstract

Artemov, Kunimoto, and Serrano (2013a,b, henceforth, AKS) study a mechanism design problem where arbitrary restrictions are placed on the set of first-order beliefs of agents. Calling these restrictions Δ, they adopt Δ-rationalizability (Battigalli and Siniscalchi, 2003) and show that Δ-incentivecompatibility and Δ-measurability are necessary and sufficient conditions for robust virtual implementation, which implies that virtual implementation is possible uniformly over all type spaces consistent with Δ-restrictions. By appropriately defining Δ in order to restrict attention to complete information environments and thereafter explicitly modelling the assumption of complete information in the language of type spaces, I re-establish the permissive implementation result of Abreu and Matsushima (1992a). However, AKS need to fix a complete information environment throughout their analysis and therefore does not enable us to ask if robust virtual implementation results are “robust” to the relaxation of the complete information environment. The main result of this paper shows that permissive robust virtual implementation results can be extended to nearby incomplete information environments. I also obtain a tight connection between the class of nearby incomplete information environments considered by this paper and that considered by Oury and Tercieux (2012).