A note on optimal contracting with public ex post information under limited liability

  • Daniel DanauEmail author
  • Annalisa Vinella
Original Paper


Riordan and Sappington (J Econ Theory 45:189–199, 1988) show that in an agency relationship in which the agent’s type is correlated with a public ex post signal, the principal may attain first best (full surplus extraction and efficient output levels) if the agent is faced with a lottery such that each type is rewarded for one signal realization and punished equally for all the others. Gary-Bobo and Spiegel (RAND J Econ 37:431–448, 2006) show that there exist locally incentive compatible lotteries such that limited liability constraints are satisfied, only if these constraints are satisfied when that kind of lottery is used. We explore how lotteries should be designed to attain not only local but also global incentive compatibility when the agent is protected by limited liability. The main issue with global incentive compatibility rests with intermediate types being potentially attractive reports to both lower and higher types. A lottery including three levels of profit (rather than only two) is found to be optimal under limited liability, in that it is most likely to be globally incentive compatible, if local incentive constraints are strictly satisfied. Conditions for first-best implementation are identified.


Informative signals Limited liability Incentive compatibility 

JEL Classification




  1. Armstrong M, Sappington DEM (2007) Recent developments in the theory of regulation. In: Armstrong M, Portier R (eds) Handbook of industrial organization, vol 3. Elsevier B.V, AmsterdamGoogle Scholar
  2. Bose S, Zhao J (2007) Optimal use of correlated information in mechanism design when full surplus extraction may be impossible. J Econ Theory 135:357–381Google Scholar
  3. Crémer J, McLean R (1988) Full extraction of the surplus in Bayesian and dominant strategy auctions. Econometrica 56(6):1247–1258Google Scholar
  4. Decker C (2015) Modern economic regulation. An introduction to theory and practice. Cambridge University Press, CambridgeGoogle Scholar
  5. Demougin D, Garvie D (1991) Contractual design with correlated information under limited liability. RAND J Econ 22:477–489Google Scholar
  6. Farsi M, Filippini, M, Plagnet M-A, Saplacan R (2010) The economies of scale in the French power distribution utilities, CEPE Working Paper No. 73. Centre for Energy Policy and Economics, Swiss Federal Institutes of TechnologyGoogle Scholar
  7. Fraas AG, Munley VG (1984) Municipal wastewater treatment cost. J Environ Econ Manag 11:28–38Google Scholar
  8. Fraquelli G, Giandrone R (2003) Reforming the wastewater treatment sector in Italy: implications of plant size, structure, and scale economies. Water Resour Res 39(10):1–7Google Scholar
  9. Gary-Bobo R, Spiegel Y (2006) Optimal state-contingent regulation under limited liability. RAND J Econ 37:431–448Google Scholar
  10. Greve T, Keiding H (2016) Regulated competition under increasing returns to scale. J Public Econ Theory 18(3):327–345Google Scholar
  11. Joskov PL (2007) Regulation of natural monopoly, chapter 16. In: Polinsky M, Shavell S (eds) Handbook of law and economics, vol 2. Elsevier, AmsterdamGoogle Scholar
  12. Kessler AS, Lulfesmann C, Schmitz PW (2005) Endogenous punishments in agency with verifiable ex post information. Int Econ Rev 46(4):1207–1231Google Scholar
  13. Laffont JJ, Tirole J (1983) A theory of incentives in procurement and regulation. MIT Press, CambridgeGoogle Scholar
  14. Lewis TR, Sappington DEM (1989) Countervailing incentives in agency problems. J Econ Theory 49:294–313Google Scholar
  15. Maggi G, Rodriguez-Clare A (1995) On countervailing incentives. J Econ Theory 66:238–263Google Scholar
  16. McAfee PR, Reny PJ (1992) Correlated information and mechanism design. Econometrica 60(2):395–421Google Scholar
  17. Myerson R (1981) Optimal auction design. Math Oper Res 6(1):58–73Google Scholar
  18. Reynès F (2017) The Cobb–Douglas function as a flexible function. Analyzing the substitution between capital, labor and energy, Sciences Po OFCE Working Paper No. 12, 2017/04/20Google Scholar
  19. Riordan M, Sappington DEM (1988) Optimal contracts with public ex post information. J Econ Theory 45:189–199Google Scholar
  20. Schmalensee R (1978) A note on economies of scale and natural monopoly in the distribution of public utility services. Bell J Econ 9(1):270–276Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Centre de Recherche en Economie et ManagementUniversité de Caen NormandieCaenFrance
  2. 2.Dipartimento di Economia e FinanzaUniversità degli Studi di Bari “Aldo Moro”BariItaly

Personalised recommendations