Collusion and Price Rigidity

Abstract

We consider an infinitely-repeated Bertrand game, in which prices are perfectly observed and each firm receives a privately-observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria (SPPE), wherein any "punishments" are borne equally by all firms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each firm is strictly increasing in its cost level: such "fully-sorting" schemes offer efficiency benefits, as they ensure that the lowest-cost firm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost firm must be deterred from mimicking a lower-cost firm by charging a lower price. A rigid-pricing scheme, where a firm's collusive price is independent of its current cost position, sacrifices efficiency benefits but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i) the absence of equilibrium-path price wars, and (ii) a rigid price. If firms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost firms may be distorted downward, in order to diminish the incentive to cheat.

JEL Classification: C73, L13, L14