Skip to main content
Log in

Robust contracting in general contract spaces

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript

Abstract

We consider a general framework of optimal mechanism design under adverse selection and ambiguity about the type distribution of agents. We prove the existence of optimal mechanisms under minimal assumptions on the contract space and prove that centralized contracting implemented via mechanisms is equivalent to delegated contracting implemented via a contract menu under these assumptions. Our abstract existence results are applied to a series of applications that include models of optimal risk sharing and of optimal portfolio delegation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aliprantis, C., Border, K.: Infinite dimensional analysis: a hitchhiker’s guide. Springer Verlag, Berlin (2006)

    Google Scholar 

  • Auster, S.: Robust contracting under common value uncertainty. Theor. Econ. 13(1), 175–204 (2018)

    Article  Google Scholar 

  • Backhoff, J., Horst, U.: Conditional analysis and a principal-agent problem. SIAM J. Financ. Math. 7(1), 477–507 (2016)

    Article  Google Scholar 

  • Balder, E., Hess, C.: Two generalizations of komlo’s theorem with lower closure-type applications. J. Convex Anal. 1(3), 25–44 (1996)

    Google Scholar 

  • Balder, E.J.: New sequential compactness results for spaces of scalarly integrable functions. J. Math. Anal. Appl. 151(1), 1–16 (1990)

    Article  Google Scholar 

  • Balder, E.J.: On the existence of optimal contract mechanisms for incomplete information principal-agent models. J. Econ. Theory 68(1), 133–148 (1996)

    Article  Google Scholar 

  • Baranov, A., Woracek, H.: Majorization in de Branges spaces. III. Division by Blaschke products. Algebra i Analiz 21(6), 3–46 (2009). https://doi.org/10.1090/S1061-0022-2010-01122-1

    Article  Google Scholar 

  • Barbu, V., Precupanu, T.: Convexity and optimization in Banach spaces. Springer, Berlin (2012)

    Book  Google Scholar 

  • Beer, G.: Topologies on closed and closed convex sets, vol. 268. Springer, Berlin (1993)

    Book  Google Scholar 

  • Berge, C.: Topological Spaces: including a treatment of multi-valued functions, vector spaces, and convexity. Courier Corporation (1963)

  • Bergemann, D., Schlag, K.: Robust monopoly pricing. J. Econ. Theory 146(6), 2527–2543 (2011)

    Article  Google Scholar 

  • Bourbaki, N.: Éléments de mathématique. I: Les structures fondamentales de l’analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale. Deuxième édition revue et augmentée. Actualités Scientifiques et Industrielles, No. 1045. Hermann, Paris (1958)

  • Brannath, W., Schachermayer, W.: A bipolar theorem for L \({} _+^ 0 (\Omega ,{\cal{F}},{\bf P}) \). In: Séminaire de Probabilités XXXIII, pp. 349–354. Springer, Berlin (1999)

  • Brooks, B., Du, S.: Optimal auction design with common values: An informationally robust approach. Unpublished manuscript, Stanford Univ., Stanford, CA (2018)

  • Carroll, G.: Robustness and linear contracts. Am. Econ. Rev. 105(2), 536–63 (2015)

    Article  Google Scholar 

  • Carroll, G.: Information games and robust trading mechanisms. Unpublished manuscript, Stanford Univ., Stanford, CA (2018)

  • Carroll, G.: Robustness in mechanism design and contracting. Ann. Rev. Econ. 11, 139–166 (2019)

    Article  Google Scholar 

  • Cvitanić, J., Schachermayer, W., Wang, H.: Utility maximization in incomplete markets with random endowment. Finance Stochast. 5(2), 259–272 (2001)

    Article  Google Scholar 

  • Du, S.: Robust mechanisms under common valuation. Econometrica 86(5), 1569–1588 (2018)

    Article  Google Scholar 

  • Föllmer, H., Schied, A.: Stochastic finance: an introduction in discrete time. Walter de Gruyter, Berlin (2011)

    Book  Google Scholar 

  • Frankel, A.: Aligned delegation. Am. Econ. Rev. 104(1), 66–83 (2014)

    Article  Google Scholar 

  • Garrett, D.F.: Robustness of simple menus of contracts in cost-based procurement. Games Econ. Behav. 87, 631–641 (2014)

    Article  Google Scholar 

  • Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18(2), 141–153 (1989)

    Article  Google Scholar 

  • Kramkov, D., Schachermayer, W.: The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. pp. 904–950 (1999)

  • Kramkov, D., Schachermayer, W.: Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 13(4), 1504–1516 (2003)

    Article  Google Scholar 

  • Maccheroni, F., Marinacci, M., Rustichini, A.: Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74(6), 1447–1498 (2006)

    Article  Google Scholar 

  • Mirrlees, J., Raimondo, R.C.: Strategies in the principal-agent model. Econ. Theor. 53(3), 605–656 (2013)

    Article  Google Scholar 

  • Ou-Yang, H.: Optimal contracts in a continuous-time delegated portfolio management problem. Rev. Financ. Stud. 16(1), 173–208 (2003)

    Article  Google Scholar 

  • Page, F.H.: Optimal contract mechanisms for principal-agent problems with moral hazard and adverse selection. Econ. Theor. 1(4), 323–338 (1991)

    Article  Google Scholar 

  • Page, F.H.: Mechanism design for general screening problems with moral hazard. Econ. Theor. 2(2), 265–281 (1992)

    Article  Google Scholar 

  • Page, F.H.: Optimal deterministic contracting mechanisms for principal-agent problems with moral hazard and adverse selection. Rev. Econ. Design 3(1), 1–13 (1997)

    Article  Google Scholar 

  • Sannikov, Y.: A continuous-time version of the principal-agent problem. Rev. Econ. Stud. 75(3), 957–984 (2008)

    Article  Google Scholar 

  • Schachermayer, W.: Optimal investment in incomplete financial markets. In: Mathematical Finance-Bachelier Congress 2000, pp. 427–462. Springer, Berlin (2002)

  • Schättler, H., Sung, J.: The first-order approach to the continuous-time principal-agent problem with exponential utility. J. Econ. Theory 61(2), 331–371 (1993)

    Article  Google Scholar 

  • Song, Y.: Efficient implementation with interdependent valuations and maxmin agents. J. Econ. Theory 176, 693–726 (2018)

    Article  Google Scholar 

  • Spear, S.E., Srivastava, S.: On repeated moral hazard with discounting. Rev. Econ. Stud. 54(4), 599–617 (1987)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees and editors for their valuable advice.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Patrick Beissner.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Horst and Beissner gratefully acknowledge financial support by the CRC TRR 190 Rationality and competition - the economic performance of individuals and firms

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Backhoff-Veraguas, J., Beissner, P. & Horst, U. Robust contracting in general contract spaces. Econ Theory 73, 917–945 (2022). https://doi.org/10.1007/s00199-021-01354-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00199-021-01354-9

Keywords

JEL Classification

Navigation