Online Appendix: The Power of Communication

According to Sannikov and Skrzypacz (2007), collusion breaks down in public Nash equilibrium. Here, though, firms collude in public communication equilibrium as long as equation (5) in the paper holds. If it fails, this agreement falls apart for the same reason as in Sannikov and Skrzypacz’s result: obedient firms cannot be identified, so discouraging overproduction requires punishing everyone whenever prices are low. By Lemma 1 of the paper, this punishment cost is of order r √ ∆t, but the benefit, in terms of current collusion, is of order r∆t. As ∆t → 0, the costs overwhelm any benefits. Nevertheless, firms can still collude in private communication equilibrium even if (5) fails, as I show next. Intuitively, firms coordinate infrequently: they agree that it takes more than one low price to trigger punishment, thus tempering punishment costs. Just which low prices trigger punishment is temporarily kept secret from firms to recycle incentives.