Tight Bounds on the Relative Performances of Pricing Mechanisms in Storable Good Markets

Abstract

In the storable good monopoly problem, a monopolist sells a storable good by announcing a price in each time period. Each consumer has a unitary demand per time period with an arbitrary valuation. In each period, consumers may buy none, one, or more than one good (in which case the extra goods are stored for future consumption incurring a linear storage cost). We compare the performance of two important pricing mechanisms on the profitability of the monopolist: pre-announced pricing mechanisms and price contingent mechanisms. In pre-announced pricing the prices in each time period are stated in advance; in a price contingent mechanism each price is stated at the start of the time period, and these prices are dependent upon past purchases. We prove that the monopolist can earn at most $O(\log T +\log N)$ times more profit by using a pre-announced pricing mechanism rather than a price contingent mechanism. Here T denotes the number of time periods and N denotes the number of consumers. This bound is tight; examples exist where the monopolist would earn a factor $\varOmega (\log T +\log N)$ more by using a pre-announced pricing mechanism.