We assess the strength of the different conditions identified in the literature of robust mechanism design. We focus on three conditions: ex post incentive compatibility, robust monotonicity, and robust measurability. Ex post incentive compatibility has been shown to be necessary for any concept...

We uncover a new necessary condition for implementation in iteratively undominated strategies by mechanisms that satisfy the “best element property” where for each agent, there exists a strategy profile that gives him the highest payoff in the mechanism. This class includes finite and...

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...