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...

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 in an independent private value first-price auction with two bidders and two possible valuations. There is a benevolent center that knows the bidders’ valuations and sends private signals to the bidders in order to maximize their expected payoffs. After...

We present a cheap talk extension to any two-player, finite, complete information game, and ask what correlations over actions are implementable in Nash equilibria of the extended game. In the extension, players communicate repeatedly through a detail-free mediator that has been studied in...