Collusion model with imperfect public monitoring

Question

It is well known that consumers' intertemporal incentives may play a key role on the potential of firms to sustain collusion. To my knowledge, most previous efforts studying the topic have assumed perfect observability of actions. How would imperfect public monitoring affect the usual results of industrial organization, regarding symmetrical punishments and price wars mechanisms? Would the results hold?

Since Coase (1972) there has been awareness that intertemporal incentives play a key role on determining industry configuration and the extent to which firms may exercise market power. Ausubel and Deneckere (1987), Gul (1987), Dutta et al. (2007) and Schiraldi and Nava (2012) analyzed this in an oligopolic setting, particularly the effect of product durability on the feasibility of sustaining a collusive agreement. Their findings nevertheless contradict Coase's, as they show that the greater the patience of forward-looking rational consumers, the easier it was for a cartel to sustain collusion.

These results, however, asume perfect observability of firms' actions. So, what would happen if we lift this (rather restrictive) assumption? I'm thinking of Dutta et al. (2007)'s model for studying a cartel in a durable goods market and considering what would happen if one would extend it into a stochastic environment, making consumer's turnover rate random, which leads to an imperfect monitoring setting.

Answer 1

You'll get different answers depending on assumptions, so the answer is maybe. Two papers come to mind.

For a continuous time model, see Sannikov and Skrzypacz (2007). They show that collusion is impossible with imperfect monitoring if new information arrives continuously and actions can respond quickly in accordance with new information.

A well known model using discrete time periods is Green and Porter (1984). They show that collusion is possible. Firms can sustain collusion by allowing for the possibility of price wars.

Answer 2

Sustained collusion in repeated games is a topic with a huge and diverse literature. Motta's book Competition Policy, Theory and Practice devotes the entire Chapter 4 to it. Chapter 2 of Whinston's Lectures on Antitrust Economics has a more high-level overview of the modern literature on price-fixing.

Apart from the mutual observability of firm's price setting, the other main complication is heterogeneity of beliefs about demand (e.g. has there been a common demand shock, or has someone deviated from the cartel?). This literature started with Green and Porter (1984) who analysed cartel self-enforcement in the presence of demand uncertainty. A similar paper is Rotemberg and Saloner (1986) who showed that price wars are more likely during times of high demand ("booms").

A recent paper is Athey and Bagwell (2001) where prices are publicly observed but each firm receives a privately observed cost shock in each period. They show that collusion can be maintained in such environments if high-cost firms (temporarily) give up market share. They also analyze the role of communication and side-payments (i.e. inter-firm bribes to enforce collusion).

Answer 3

Besides the one answer with a couple references, I haven't got anything else. I've been developing a model like the one posted on my question and I'm leaving here what I've found, in case anyone finds it useful. Now, developing a fully blown model is beyond the scope of a single answer, but I'll try to lay down my conclusions so far.

Taking Dutta et al. (2007)'s model and expanding it with some simple assumptions to develop imperfect observability of actions among firms seems to show that "price wars" may be an inefficiently costly discipline mechanism in this setting, even when compared to other strongly symmetrical punishments. Not only the characteristics of continuations payoffs count, but also the actual discipline procedure matters. The reason for this is that when equilibrium "price wars" are used to enforce the agreement consumers will tend to delay purchase and wait until a bad realization of demand forces firms to switch phase to buy cheaper, undermining collusive profits.

Broadly speaking, the fact that equilibrium "price wars" shift consumers' intertemporal incentives may have implications on the collusive outcome.