Pacman Refutes the Coase Conjecture: Durable-Goods Monopoly with Discrete Demand

Abstract

We analyze a dynamic game between consumers with unit demands and the sole seller of a durable good. Unlike previous analyses, we assume there exists a finite collection of buyers rather than a continuum. We show that none of the main conclusions of the durable-goods literature survives this change in assumption. In particular, for any demand curve there exists a subgame-perfect equilibrium such that for discount factors near one the monopolist's profit approaches the profit attainable under perfect price discrimination. This contradicts Coase's conjecture (1972)--proved formally for the continuum case by Gul, Sonnenschein, and Wilson (1986)--that the monopolist's profit must always converge to zero. It also implies that renting or precommitting to a path of prices-which Bulow (1982) and Stokey (1979) have shown, respectively, must always increase profit with a continuum of buyers--may strictly reduce profits when the collection of buyers is finite. Hence, while in other contexts the assumption of a continuum of consumers has proved an innocuous and useful simplification, in the context of durable-goods monopoly it has proved misleading.