A Dynamic Theory of Random Price Discounts

A seller with commitment power sets prices over time. Risk-averse buyers arrive to the market and decide when to purchase. We show that it is optimal for the seller to choose a constant high price punctuated by occasional episodes of sequential discounts that occur at random times. This optimal price-path has the property that the price a buyer ends up paying is independent of his arrival and purchase times, and only depends on his valuation. Our theory accommodates empirical findings on the timing of discounts.