Ex-post implementation with interdependent values

We characterize ex-post implementable allocation rules for single object auctions under quasi-linear preferences with interdependent value functions. We show that requiring ex-post implementability is equivalent to requiring a weakening of monotonicity, which is a familiar condition used to characterize dominant strategy implementation. We illustrate that non-monotone rules may be necessary to achieve objectives such as efficiency and revenue maximizations, even in standard models such as the maximum signal model studied in Bulow and Klemperer (2002), and Bergemann et al. (2020).