Robustness Foundations for B-IC

Standard Mechanism Design has generated many powerful predictions. These predictions however often rely on strong knowledge assumption imposed about agents beliefs on the designer and are not robust to changes in those beliefs. At the other extreme, the belief-free approach has maximally relaxed these strong knowledge assumptions by instead imposing no restrictions. Previous work by Ollar and Penta has facilitated studying an intermediate ground of robustness by introducing the notion of a belief restriction describing what the designer is willing to assume about agents beliefs. They study implementation questions under a suitable generalisation of ex post equilibrium. Ex post equilibrium however does not allow the designer to elicit beliefs and one could consider other solution concepts. A natural alternative is to consider Bayes Nash equilibrium, allowing the designer to elicit beliefs whenever such belief elicitation facilitates implementation. Robustness then requires implementation to be possible across all type spaces consistent with the belief restriction. In this project we establish that separable environments are a sufficient condition for these two notions of robustness to be equivalent.