Collusion and Price Rigidity

Abstract

We consider an infinitely repeated Bertrand game, in which prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria, 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. When the model is modified to include i.i.d. public demand shocks, the downward pricing distortion that accompanies a firm's lower‐cost realization may occur only when current demand is high.

Optimal collusion with internal contracting

“…Following this tool, each firm's PPE payoff is factored into two components, current-period profit and (discounted) expected continuation values that are conditional on current-period actions, and after any history, the set of continuation values is equal to the equilibrium-value set. We next follow Athey and Bagwell (2001) and Athey et al (2004), who show that existing tools from (static) mechanism design theory can be used to find the solution of the factored program. We finally establish a two-tier mechanism design program.…”

“…An important feature in recent theoretical work is that the state of firms' production costs is regarded as private information. Aoyagi (2003), Bagwell (2001, 2006), Athey et al (2004) and Skrzypacz and Hopenhayn (2004) develop models of this kind, where firms play a repeated Bertrand pricing game or repeated procurement auctions. 2 Despite their rich analyses of collusion, those theoretical models have given no attention to the possibility that the location private information is the hired agents who produce firms' outputs.…”

“…Our paper develops a model of collusion in which two firms play an infinitely-repeated Bertrand game, and uses work by Athey and Bagwell (2001) and Athey et al (2004) as a benchmark. Following their models, we consider the environment in which firm actions are publicly observed.…”

“…5 Interestingly, these contrasting incentives can work to the colluding firms' advantage. 6 Consider first the effect of collusion on internal contract. If colluding firms coordinate to allocate market shares by the criterion of productive efficiency, then a low-cost agent who reports high cost will be paid nothing (because of no production) when the other firm announces low cost.…”

“…For a classic evidence on agent's overstating behavior, see Schiff and Lewin (1970), and for agent's cost-padding behavior, see Laffont and Tirole (1993). 6 The contrasting incentives between informed and uninformed parties differ from the "countervailing incentives"…”