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Noisy observation in adverse selection models

  • Caillaud, Bernard
  • Guesnerie, Roger
  • Rey, Patrick

We consider a principal-agent contracting problem under incomplete information where some of the agent's actions are imperfectly observable. Contracts take the form of reward schedules based on the noisy observation of the agent's action. We first review situations where the principal can reach the same utility as in the absence of noise. Then we focus on the use of linear reward schedules, which allow universal implementation, i.e. implementation of a given mechanism for any unbiased noise of observation, and on quadratic reward schedules, which only require the knowledge of the variance of the noise. We exhibit sufficient conditions under which linear reward schedules implement a given mechanism. Finally, we characterize necessary conditions for a mechanism to be implementable under noisy observation by a linear schedule, and by quadratic schedules. We give the geometric intuition behind all results.

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Paper provided by CEPREMAP in its series CEPREMAP Working Papers (Couverture Orange) with number 8921.

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Length: 33 pages
Date of creation: 1989
Date of revision:
Handle: RePEc:cpm:cepmap:8921
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  1. Roger B. Myerson, 1977. "Incentive Compatability and the Bargaining Problem," Discussion Papers 284, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Picard Pierre, 1986. "On the design of incentive schemes under moral hazard and adverse selection," CEPREMAP Working Papers (Couverture Orange) 8602, CEPREMAP.
  3. Melumad, Nahum D. & Reichelstein, Stefan, 1989. "Value of communication in agencies," Journal of Economic Theory, Elsevier, vol. 47(2), pages 334-368, April.
  4. Peter J. Hammond, 1979. "Straightforward Individual Incentive Compatibility in Large Economies," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 263-282.
  5. Bengt Holmstrom & Paul R. Milgrom, 1985. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Cowles Foundation Discussion Papers 742, Cowles Foundation for Research in Economics, Yale University.
  6. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
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