Multidimensional screening: online computation and limited information

Optimal screening has been studied in economics, game theory, and recently computer science. We study the problem in a nonlinear pricing application, where a monopoly designs a price schedule from which the buyers self-select the quality they wish to consume. We formulate a multidimensional model with buyers' utility functions that need not satisfy the standard single-crossing assumption. We characterize the solution with the first-order optimality conditions and present a framework for analyzing the solution. With the framework, the structure of the solution is easily illustrated and the sensitivity analysis can be done. We give numerical examples that demonstrate the properties of the solution. With these observations, we discuss the complexity of the problem and solving the problem under limited information. We examine what information the monopoly needs when adjusting the price schedule to increase the profit. This paper applies, e.g., to pricing situations in electronic commerce where the seller may have limited information available, and the seller learns about the buyers' preferences online when doing the business.

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