(Regular readers of this blog will know that I consider that a good thing.)

John Lazarev at Stanford GSB has a nice little theory paper (not his job market paper which is not little and not theory, but also nice.)  It’s a model of market competition which consists of two stages.  In stage one the firms simultaneously and non-cooperatively choose subsets of prices.  The interpretation is that the firm is restricting itself to later choose only prices from the restricted set.  After seeing the restriction sets each firm has chosen the firms then simultaneously choose prices from their respective sets.

This is a stylized model of the way “competition” works between airlines:

Almost every major US airline has independent pricing and yield (revenue) management departments. That operates as follows. The pricing department sets prices for each seating class (e.g. up to 6 non-refundable economy class fares) starting many days from the actual flight. These prices are subsequently updated very rarely. The revenue management department treats the prices as given but decides three times a day which of the fare classes to make available for purchase and which to keep closed. According to industry insiders, these departments do not actively interact with each other. Thus, there exist two stages of decision making. Effectively, the pricing department commits to a subset of prices, while the revenue management department chooses a price from this subset.

Its also a great question for a future prelim.  Construct an equilibrium (subgame-perfect please) in which the firms effectively collude and earn monopoly profits.

Simple.  (I will assume symmetric linear cost homogeneous product price-competition because it makes the argument simple and also quite stark:  standard Bertrand pricing leads to cutthroat competitition and zero profits.) In the first stage each firm restricts to only two prices:  the monopoly price and marginal cost pricing. If nobody deviates from this then all firms set the monopoly price.  If anybody deviates from this by either excluding the monopoly price or including an intermediate price then all firms set the lowest price in their chosen set.  All other deviations are ignored.

Its easy to check that this is a subgame perfect equilibrium and all firms earn monopoly profits.  Lazarev does the same for a more general model of differentiated products price competition.