Time-Differentiated Monopolies

We consider sequential competition among sellers, with different consumers desiring the good at different times. Each consumer has the option of buying from a later seller. Each seller recognizes that future sellers are potential competitors. We find that if sellers do not know the previous history of sales, then an equilibrium price is necessarily the same as that which would be set by a simple monopolist who expects no future sellers. Even if the sellers know more about the history of sales, their monopoly prices are still equilibrium prices unless arrivals of two sellers in very short succession are possible. If, however, the sellers are fully informed about the history, then there are also equilibria with lower prices, which are supported by consumers’ strategies with an increasing relation between the price and the propensity to defer buying the good. Such strategies pose a credible, effective, threat to sellers who contemplate setting high prices.