Summary
We study the problem faced by an incomplete information monopolist seeking to design a line of contracts so as to simultaneously screen consumers by type and resolve the moral hazard problems associated with contract performance. We formulate the monopolist's problem as a mechanism design problem in which the set of consumer types is taken to be a Polish space, and the contract space an arbitrary compact metric space. Allowing for risk aversion on the part of the monopolist and consumers, and taking as the feasible set of mechanisms the collection of all measurable functions defined on the space of consumer types with values in the space of contracts, we present a new characterization of incentive compatibility in an infinite dimensional setting which allows us to reformulate the monopolist's design problem as an unconstrained optimization problem (i.e., as a problem without the incentive compatibility contraints). Using simple techniques, we then demonstrate the existence of an optimal screening mechanism for the monopolist. We thus extend the existing analysis of the incomplete information monopoly problem to an infinite dimensional setting with moral hazard, and we provide an existence result not available in the existing literature.
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I thank seminar participants at Indiana University, McGill University, and the University of Calgary for helpful comments. I also thank Kerry Back, Bob Becker, Praveen Kumar, Mark Johnson, Ramon Marimon, Murat Sertel, Bill Sealey, Gordon Sick, and Nicholas Yannelis for helpful comments. The comments and suggestions of an anonymous referee are especially appreciated. I am solely responsible for any errors.
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Page, F.H. Mechanism design for general screening problems with moral hazard. Econ Theory 2, 265–281 (1992). https://doi.org/10.1007/BF01211443
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DOI: https://doi.org/10.1007/BF01211443