Collusion model with imperfect public monitoring 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.
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.