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...

Two players can make use of a trusted third party who mediates and partially resolves their conflict. Usually, the mediator should be aware of the situation and give suggestions to the players accordingly. However, a corrupt mediator can have a big influence on the outcome of the game. We single...

We explore in an equilibrium framework whether games with multiple Nash equilibria are easier to play when players can communicate. We consider two variants, modelling talk about future plans and talk about past actions. The language from which messages are chosen is endogenous, messages are...

We show that essentially every communication equilibrium of any finite Bayesian game with two players can be implemented as a strategic form correlated equilibrium of an extended game, in which before choosing actions as in the Bayesian game, the players engage in a possibly infinitely long (but...

Games with multiple Nash equilibria are believed to be easier to play if players can communicate. We present a simple model of communication in games and investigate the importance of when communication takes place. Sending a message before play captures talk about intentions, after play...