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Variable preference relations: Existence of maximal elements

Author

Listed:
  • Dinh The Luc

  • Antoine Soubeyran

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider variable preference relations, also called reference dependent preference relations, which are typical in the study of dynamic models in economic theories. We introduce a new concept of weak consistency, a generalization of acyclicity, as an immediate regret condition for variable preferences. The main result to establish is on an existence criterion for maximal elements of a space equipped with a weakly consistent variable preference relation. It is expressed via a preference completeness condition which is equivalent to existence of aspiration points. As applications, we show that a number of results known in the recent literature on maximum principles on a space with or without topological structure can be obtained from the unifying approach of this paper. Habit formation and state functions are also discussed in the framework of variable preference relations.

Suggested Citation

  • Dinh The Luc & Antoine Soubeyran, 2013. "Variable preference relations: Existence of maximal elements," Post-Print hal-01500879, HAL.
    • Handle: RePEc:hal:journl:hal-01500879
    DOI: 10.1016/j.jmateco.2013.05.004
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    Cited by:

    1. Shokouh Shahbeyk & Majid Soleimani-damaneh & Refail Kasimbeyli, 2018. "Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure," Journal of Global Optimization, Springer, vol. 71(2), pages 383-405, June.
    2. Gianni Bosi & Magalì E. Zuanon, 2017. "Maximal elements of quasi upper semicontinuous preorders on compact spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 109-117, April.
    3. Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.
    4. T. Q. Bao & B. S. Mordukhovich & A. Soubeyran, 2015. "Variational Analysis in Psychological Modeling," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 290-315, January.
    5. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 931-946, December.
    6. Haoyang Wu, 2023. "Constructing a type-adjustable mechanism to yield Pareto-optimal outcomes," Papers 2309.01096, arXiv.org, revised Dec 2023.

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