In a theoretical investigation of durable goods monopolies Bagnoli, Sagant and Swierbinski (1989) show that when the monopolistic seller faces a discrete demand he can even perfectly price discriminate between buyers over time. So contrary to Coases? conjecture a monopolistic durable goods seller does not loose his monopoly power and can even extract more than the usual monopoly profit.

The authors used a dynamic framework to model the game between consumers and a single seller. The seemingly innocuous assumption of using a finite collection of buyers instead of a continuum of buyers changes their results dramatically from the standard exposition of the theory. Coase's conjecture that a durable-goods monopolist cannot earn supracompetitive profits in the continuous-time limit, Bulow's proposition that renting a durable is always more profitable than selling it, and Stokey's proposition that precommitting to a time path of prices is always optimal all turn out to be false when the set of buyers is finite.

The seller?s strategy in their model is called the ?Pacman strategy? as the seller?s price goes down the demand curve extracting all rents in the market. The monopolist sets the price in each period to the highest remaining reservation price and lowers it if and only if all buyers with the highest reservation price have purchased the good. If the monopolist plays the Pacman strategy, then no buyer can achieve positive utility. So a buyer of type V_lwould accept the monopolist's offer as a sequential best response at an information set where offered price is less than V_l if that information set is reached.

Bagnoli, Salant, Swierbinski (1989). Durable Goods Monopoly with Discrete Demand, Journal of Political Economy, 97: 1459-78.