Continuous Level-k Mechanism Design

In de Clippel et al. (2019), it is shown that, perhaps surprisingly, the set of implementable social choice functions essentially same whether agents have bounded depth reasoning or rational expectations. The picture quite different when taking into account possibility small modeling mistakes. While continuous (strict) equilibrium implementation becomes very demanding (Oury and Tercieux (2012) – OT), continuity in level-k obtains for free. A decomposition conditions implied by OT notion confirms that use equilibrium, not per se, responsible difference.