Nonlinear Pricing and Mechanism Design

In applications of theories of incentives, the information known privately by an economic agent is represented by a point in a Euclidean space. Other agents know the probability distribution of this point, but not its realization, which is called the agent’s type. For models of this sort, designs of optimal incentive schemes present few difficulties when agents’ types are one-dimensional. The computational difficulties are severe, however, when the types are multidimensional. When the types are m -dimensional, the main task is to solve a family of partial differential equations to obtain a map : < ! < that provides the Lagrange multipliers for each type’s incentive-compatibility constraints. This chapter describes methods for solving simple versions that arise in nonlinear pricing and mechanism design. The exposition concentrates initially on nonlinear pricing, but later the similar problems that arise in mechanism design are described briefly.