Evaluating the Conditions for Robust Mechanism Design

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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 of robust implementation, while robust monotonicity and robust measurability have been shown to be necessary for robust (full) exact and virtual implementation, respectively. This paper shows that while violations of ex post incentive compatibility and robust monotonicity do not easily go away, we identify a mild condition on environments in which robust measurability is satisfied by all social choice functions over a residual set (i.e., a countable intersection of open and dense sets) of first-order types. We conclude that, to the extent that ex post incentive compatibility is permissive, robust virtual implementation can be significantly more permissive than robust exact implementation.