[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

We study reference-dependent preference relations defined by a real-valued bivariate function and prove an existence criterion for maximal elements. Then we formulate a generalized version of the well-known Brondsted maximum principle and apply it to behavioral traps and Nash equilibrium in games with preference relations that are not necessarily partial orders.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Koszegi, B., Rabin, M.: A model of reference-dependent preferences. Q. J. Econ. 121(4), 1133–1166 (2006)

    Google Scholar 

  2. Soubeyran, A.: Variational rationality, a theory of individual stability and change: worthwhile and ambidextry behavior. Mimeo (2009)

  3. Brondsted, A.: On a lemma of Bishop and Phelps. Pac. J. Math. 55, 335–341 (1974)

    Article  MathSciNet  Google Scholar 

  4. Aleskerov, F., Bouyssou, D., Monjardet, B.: Numerical representations of binary relations with thresholds: a brief survey 1 (2009). www.lamsade.dauphine.fr/dea103/ens/bouyssou/FABM.pdf

  5. Soubeyran, A.: Variational rationality and the unsatisfied man: routines and the course pursuit between aspirations, capabilities and beliefs. Mimeo (2010)

  6. Luc, D.T., Soubeyran, A.: Variable Preferences Relations: Existence of Maximal Elements (2010). Preprint. hal-00621272

  7. Bossert, W., Suzumura, K.: Social norms and rationality of choice. Working paper. Discussion paper series, No. 208. Université de Montreal, COE/RES (2007)

  8. Simon, H.A.: A behavioral model of rational choice. Q. J. Econ. 69, 99–118 (1955)

    Article  Google Scholar 

  9. Simon, H.A.: Models of Man: Social and Rational. Wiley, New York (1957)

    MATH  Google Scholar 

  10. Simon, H.A.: From substantive to procedural rationality. In: Latsis (ed.) Methods and Appraisal in Economics (1967)

    Google Scholar 

  11. Simon, H.A.: Rationality as a process and product of thought. Am. Econ. Rev. 68, 1–16 (1978)

    Google Scholar 

  12. Simon, H.A.: The Science of the Artificial, 2nd edn. MIT Press, Cambridge (1982)

    Google Scholar 

  13. Simon, H.A.: Reason in Human Affairs. Stanford University Press, Stanford (1983)

    Google Scholar 

  14. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–292 (1979)

    Article  MATH  Google Scholar 

  15. Tversky, A., Kahneman, D.: Loss aversion in riskless choice: a reference dependent model. Q. J. Econ. 106, 1039–1061 (1991)

    Article  Google Scholar 

  16. Flores-Bazán, F., Hernández, E., Novo, V.: Characterizing efficiency without linear structure: a unified approach. J. Glob. Optim. 41, 43–60 (2008)

    Article  MATH  Google Scholar 

  17. Lindblom, C.E.: The science of muddling through. PAR, Public Adm. Rev. 19(2), 79–88 (1959)

    Article  Google Scholar 

  18. Greve, W.: Traps and gaps in action explanation: theoretical problems of a psychology of human action. Psychol. Rev. 108(2), 435–451 (2001)

    Article  MathSciNet  Google Scholar 

  19. Koszegi, B.: Utility from anticipation and personal equilibrium. Econ. Theory 44, 414–434 (2010)

    Article  MathSciNet  Google Scholar 

  20. Gul, F., Pesendorfer, W.: The revealed preference implications of reference dependent preferenes. Mimeo, Princeton University (2006)

  21. Luc, D.T.: On Nash equilibrium. I. Acta Math. Acad. Sci. Hung. 40(3–4), 267–272 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  22. Luc, D.T.: On Nash equilibrium. II. Acta Math. Hung. 41(1–2), 61–66 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  23. Attouch, H., Redont, P., Soubeyran, A.: A new class of alternating proximal minimization algorithms with costs-to-move. SIAM J. Optim. 18, 1061–1081 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Alternating proximal algorithms for weakly coupled convex minimization problems. Applications to dynamical games and PDE’s. J. Convex Anal. 15, 485–506 (2008)

    MathSciNet  MATH  Google Scholar 

  25. Attouch, H., Soubeyran, A.: Local search proximal algorithms as decision dynamics with costs to move. Set-Valued Var. Anal. 19(1), 157–177 (2010)

    Article  MathSciNet  Google Scholar 

  26. Chen, Y., Gazzale, R.: When does learning in games generate convergence to Nash equilibria? The role of supermodularity in an experimental setting. Am. Econ. Rev. 94, 1505–1535 (2004)

    Article  Google Scholar 

  27. Bianchi, M., Kassay, G., Pini, R.: Existence of equilibria via Ekeland’s principle. J. Math. Anal. Appl. 305, 502–512 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Flores-Bazán, F., Gutierrez, C., Novo, V.: A Brezis–Browder principle on partially ordered spaces and related ordering theorems. J. Math. Anal. Appl. 375, 245–260 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

F. Flores-Bazán acknowledges partial support by FONDECYT 110-0667 and BASAL Projects, CMM, Universidad de Chile and Centro de Investigacion en Ingenieria matematica (CI2MA).

This paper was partially written during the stay of the second author at the University of Concepcion under a research grant of CONICYT through a BASAL Project.

Author information

Authors and Affiliations

  1. CI2MA, Departamento de Ingeniería Matemática, University of Concepcion, Concepcion, Chile

    Fabián Flores-Bazán

  2. LANG, University of Avignon, Avignon, France

    Dinh The Luc

  3. GREQAM, University of Aix-Marseille, Marseille, France

    Antoine Soubeyran

Authors
  1. Fabián Flores-Bazán
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dinh The Luc
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antoine Soubeyran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabián Flores-Bazán.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Flores-Bazán, F., Luc, D.T. & Soubeyran, A. Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games. J Optim Theory Appl 155, 883–901 (2012). https://doi.org/10.1007/s10957-012-0100-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-012-0100-z

Keywords

Search

Navigation