Price asymptotics

This paper examines the pricing decisions of a seller facing an unknown demand function. It is assumed that partial information, in the form of an independent random sample of values, is available. The optimal price for the inferred demand satisfies a consistency property—as the size of the sample increases, the maximum profit and price approach the values for the case where demand is known. The main results deduced here are asymptotics for prices. Prices converge at a rate of O _p (n ^−1/3) with a limit that can be expressed as a functional of a Gaussian process. Implications for the comparison of mechanisms are discussed.