We analyze the canonical nonlinear pricing model with limited information. A seller oﬀers a menu with a ﬁnite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal ﬁnite menu for the socially eﬀicient and the revenue-maximizing mechanism. In both cases, we provide an estimate of the loss resulting from the usage of a ﬁnite n-class menu. We show that the losses converge to zero at a rate proportional to 1/n2 asn becomes large.
Bergemann, Dirk; Shen, Ji; Xu, Yun; and Yeh, Edmund M., "Mechanism Design with Limited Information: The Case of Nonlinear Pricing" (2010). Cowles Foundation Discussion Papers. 2116.