We prove that a social choice function is repeatedly implementable if and only if it is dynamically monotonic when the number of agents is at least three. We show how to test dynamic monotonicity by building an associated repeated game. It follows that a weaker version of Maskin monotonicity is...

We study optimal bidder collusion at first-price auctions when the collusive mechanism only relies on signals about bidders' valuations. We build on Fang and Morris (2006) when two bidders have low or high private valuation of a single object and additionally each receives a private noisy signal...

We present an extension to any finite complete information game with two players. In the extension, players are allowed to communicate directly and, additionally, send private messages to a simple, detail-free mediator, which, in turn, makes public announcements as a deterministic function of...