Knightian Robustness of Single-Parameter Domains

Abstract

We consider players that have very limited knowledge about their own valuations. Specifically, the only information that a Knightian player $i$ has about the profile of true valuations, ${\theta }^{\ast }$, consists of a set of distributions, from one of which ${\theta }_i^{\ast }$ has been drawn. We prove a ``robustness'' theorem for Knightian players in single-parameter domains: every mechanism that is weakly dominant-strategy truthful for classical players continues to be well-behaved for Knightian players that choose undominated strategies.

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