Continuous level-k mechanism design

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