In private-value auction environments, Chung and Ely (2007) establish maxmin and Bayesian foundations for dominant-strategy mechanisms. We first show that similar foundation results for ex post mechanisms hold true even with interdependent values if the interdependence is only cardinal. This includes, for example, the one-dimensional environments of Dasgupta and Maskin (2000) and Bergemann and Morris (2009b). Conversely, if the environment exhibits ordinal interdependence, which is typically the case with multi-dimensional environments(e.g., a player's private information comprises a noisy signalof the common value of the auctioned good and an idiosyncraticprivate-value parameter), then in general, ex post mechanisms do not have foundation. That is, there exists a non-ex-post mechanism that achieves strictly higher expected revenue than the optimal ex post mechanism, regardless of the agents' high-order beliefs.
Takuro Yamashita, and Shuguang Zhu, “On the Foundations of Ex Post Incentive Compatible Mechanisms”, TSE Working Paper, n. 18-938, July 2018.
TSE Working Paper, n. 18-938, July 2018