Implementation with ex post hidden actions

We study implementation in settings where agents take strategic actions that influence preferences over mechanism outcomes and yet are hidden from the mechanism designer. We show that such settings can arise in entry auctions for markets, and that the Vickery-Clarke-Groves mechanism is not necessarily truthful. In this paper we first formalize so-called ex post hidden actions, we then characterize social choice functions that can be implemented in a way that is robust with respect to ex post hidden actions, and finally we propose a mechanism to do so. The model allows agents to have multi-dimensional types and to have quasi-linear utilities in money. We showcase these results by identifying social choice functions that can and cannot be implemented in entry auctions for Cournot competition models.