Advertisement

Economic Theory

, Volume 2, Issue 2, pp 265–281 | Cite as

Mechanism design for general screening problems with moral hazard

  • Frank H. PageJr
Research Articles

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.

Keywords

Risk Aversion Incomplete Information Mechanism Design Moral Hazard Unconstrained Optimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ash, R.A.: Real analysis and probability. New York: Academic Press 1972Google Scholar
  2. Berge, C.: Topological spaces. New York: MacMillan 1963Google Scholar
  3. Himmelberg, C.J.: Measurable relations. Fundam, Math.LXXXVII, 53–72 (1975)Google Scholar
  4. Himmelberg, C.J., Parthasarathy, T., VanVleck, F.S.: Optimal plans for dynamic programming problems. Math. Operat. Res.1, 390–394 (1976)Google Scholar
  5. Holmstrom, B.: On the theory of delegation. In: Boyer, M., Kihlstrom, R. (eds.) Bayesian models in economic theory. Amsterdam: North Holland 1984Google Scholar
  6. Ionescu Tulcea, A: On pointwise convergence, compactness, and equicontinuity in the lifting topology I. Z. Wahrscheinlichkeitstheor. Verw. Geb.26, 197–205 (1973)Google Scholar
  7. Maitra, A.: Discounted dynamic programming on compact metric spaces, Sankhya Ser. A30, 211–216 (1968)Google Scholar
  8. Maskin, E.S., Riley, J.: Monopoly with incomplete information. Rand J. Econ.15, 171–196 (1984)Google Scholar
  9. Mathews, S., Moore J.: Monopoly provision of quality and warranties: an exploration in the theory of multidimensional screening. Econometrica55, 441–467 (1987)Google Scholar
  10. McAfee, R.P., McMillan J.: Multidimensional incentive compatibility and mechanism design. J. Econ. Theory46, 335–354 (1988)Google Scholar
  11. Myerson, R.B.: Optimal coordination mechanisms in generalized principal-agent problems. J. Math. Econ.10, 67–81Google Scholar
  12. Nowak, A.S.: On Zero-sum stochastic games with general state space I. Probab. Math. Stat.IV, 13–32 (1984)Google Scholar
  13. Page Jr., F.H.: The existence of optimal contracts in the principal-agent model. J. Math. Econ.16, 57–167 (1987)Google Scholar
  14. Parthasarathy, K.R.: Probability measures on metric spaces. New York: Academic Press 1967Google Scholar
  15. Protter, M.H., Morrey Jr., C.B.: A first course in real analysis. Berlin Heidelberg New York: Springer 1977Google Scholar
  16. Yannelis, N.C.: Set-valued functions of two variables in economic theory. In: Khan, M.A., Yannelis, N.C., (eds.) Equilibrium theory in infinite dimensional spaces. Berlin Heidelberg New York: Springer 1991Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Frank H. PageJr
    • 1
  1. 1.Department of FinanceUniversity of AlabamaTuscaloosaUSA

Personalised recommendations