Skip to main content
SpringerLink
Log in

Efficiency and equilibria in games of optimal derivative design

  • Published:
Mathematics and Financial Economics Aims and scope Submit manuscript

Abstract

In this paper, optimal derivative design when multiple firms compete for heterogenous customers is studied. Ties in the agents’ best responses generate discontinuous payoffs. Efficient tie-breaking rules are considered: In a first step, the model presented by Carlier et al. (Math Financ Econ 1:57–80, 2007) is extended, and results of Page and Monteiro (J Math Econ 39:63–109, 2003, J Econ Theory 134:566–575, 2007, Econ Theory 34:503–524, 2008) are used to prove the existence of (mixed-strategies) Nash equilibria. In a second step, the case of risk minimizing firms is studied. Socially efficient allocations are introduced, and their existence is proved. In particular, the entropic risk measure is considered.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aliprantis C., Border K.: Infinite Dimensional Analysis, a Hitchhiker’s guide, 3rd edn. Springer, New York (2006)

    MATH  Google Scholar 

  2. Armstrong M.: Multiproduct nonlinear pricing. Econometrica 64, 51–75 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bagh A., Jofré A.: Reciprocal upper semicontinuity and better reply secure games, a comment. Econometrica 74, 1715–1721 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Barrieu P., El Karoui N.: Inf-convolution of risk measures and optimal risk transfer. Financ. Stoch. 9, 269–298 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cheridito P., Li T.: Dual characterization of properties of risk measures in Orlicz hearts. Math. Financ. Econ. 2, 29–55 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Carlier G., Ekeland I., Touzi N.: Optimal derivatives design for mean-variance agents under adverse selection. Math. Financ. Econ. 1, 57–80 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dasgupta P., Maskin E.: The existence of equilibrium in discontinuous economic games, I: theory. Rev. Econ. Stud. 53, 1–26 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ekeland I., Moreno-Bromberg S.: An algorithm for computing solutions of variational problems with global convexity constraints. Numer. Math. 115, 45–69 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Föllmer, H., Schied, A.: Stochastic Finance. An Introduction in Discrete Time. de Gruyter Studies in Mathematics, vol. 27 (2004)

  10. Fudenberg D., Tirole J.: Game Theory. MIT Press, Cambridge (1991)

    Google Scholar 

  11. Horst U., Moreno-Bromberg S.: Risk minimization and optimal derivative design in a principal agent game. Math. Financ. Econ. 2, 1–27 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jouini E., Schachermeyer W., Touzi N.: Optimal risk sharing for law invariant monetary utility functions. Math. Financ. 18, 269–292 (2008)

    Article  MATH  Google Scholar 

  13. Martimort D., Stole L.: The revelation and delegation principles in common agency games. Econometrica 70, 1659–1673 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Milgrom P., Segal I.: Envelope theorems for arbitrary choice sets. Econometrica 70, 583–601 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mussa M., Rosen S.: Monopoly and product quality. J. Econ. Theory 18, 301–317 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  16. Nessah, R., Tian, G.: The Existence of Equilibria in Discontinuous and Nonconvex Games. Working Paper, http://ideas.repec.org/p/ies/wpaper/e200814.html (2010)

  17. Page F. Jr.: Catalogue competition and stable nonlinear prices. J. Math. Econ. 44, 822–835 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Page F. Jr, Monteiro P.: Three principles of competitive nonlinear pricing. J. Math. Econ. 39, 63–109 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Page F. Jr., Monteiro P.: Uniform payoff security and nash equilibrium in compact games. J. Econ. Theory 134, 566–575 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Page F. Jr., Monteiro P.: Catalogue competition and nash equilibrium in nonlinear pricing games. Econ. Theory 34, 503–524 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Phelps R.: Convex Functions, Monotone Operators and Differentiability: Lecture Notes in Mathematics, vol. 1364. Springer, New York (1989)

  22. Reny P.: On the existence of pure and mixed strategy equilibria in discontinuous games. Econometrica 67, 1029–1056 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Rochet J.-C., Choné P.: Ironing, sweeping and multidimensional screening. Econometrica 66, 783–826 (1988)

    Article  Google Scholar 

  24. Tian, G.: The Existence of Equilibria in Games with Arbitrary Strategy Spaces and Payoffs: A Full Characterization. Working paper, http://ideas.repec.org/p/cla/levarc/814577000000000160.html (2009)

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Ulrich Horst

  2. Institut für Banking und Finance, Universität Zürich, Plattenstraße 32, 8032, Zurich, Switzerland

    Santiago Moreno-Bromberg

Authors
  1. Ulrich Horst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Santiago Moreno-Bromberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Santiago Moreno-Bromberg.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Horst, U., Moreno-Bromberg, S. Efficiency and equilibria in games of optimal derivative design. Math Finan Econ 5, 269–297 (2011). https://doi.org/10.1007/s11579-012-0066-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11579-012-0066-5

Keywords

JEL Classification

Search

Navigation