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Noisy observation in adverse selection models

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

Abstract

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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Suggested Citation

  • Caillaud, Bernard & Guesnerie, Roger & Rey, Patrick, 1989. "Noisy observation in adverse selection models," CEPREMAP Working Papers (Couverture Orange) 8921, CEPREMAP.
    • Handle: RePEc:cpm:cepmap:8921
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    References listed on IDEAS

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    1. Melumad, Nahum D. & Reichelstein, Stefan, 1989. "Value of communication in agencies," Journal of Economic Theory, Elsevier, vol. 47(2), pages 334-368, April.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    4. Peter J. Hammond, 1979. "Straightforward Individual Incentive Compatibility in Large Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 263-282.
    5. 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.
    6. Picard, Pierre, 1987. "On the design of incentive schemes under moral hazard and adverse selection," Journal of Public Economics, Elsevier, vol. 33(3), pages 305-331, August.
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