Nonlinear price discrimination with a finite number of consumers and constrained recontracting

In the monopoly nonlinear pricing problem with unobservable consumer types, we study mechanisms in which the firm makes the set of consumer options conditional on the aggregate reports of consumer types it receives. Previous mechanisms that exploit knowledge of the true type distribution often have multiple equilibria or use noncredible contracts off the equilibrium path. When the monopolist can replace contracts after initial reports subject to the constraint that truthful consumers are not made worse off, the outcome is essentially the same as when the monopolist has full information. This holds whether or not the monopolist can make offers to consumers who reject all original contract offers. When the monopolist must guarantee nonnegative surplus to all truthful consumers in all contingencies, the equilibrium outcome has undistorted contracts but lower profits for the monopolist.