Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine

Abstract

We study a mechanism design problem where arbitrary restrictions are placed on the sets of first-order beliefs of agents. Calling these restrictions δ, we use δ-rationalizability (Battigalli and Siniscalchi, 2003, [5]) as our solution concept, and require that a mechanism virtually implement a socially desirable outcome. We obtain two necessary conditions, δ-incentive compatibility and δ-measurability and show that the latter is satisfied as long as a particular zero-measure set of first-order beliefs is ruled out. In environments allowing small transfers of utility among agents, these two conditions are also sufficient. © 2012 Elsevier Inc.