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Abstract regularized equilibria: application to Becker’s household behavior theory

Author

Listed:
  • J.X. Cruz Neto

    (UFPI - Universidade Federal do Piauí)

  • J. O. Lopes

    (UFPI - Universidade Federal do Piauí)

  • Antoine Soubeyran

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • João Carlos O. Souza

    (UFPI - Universidade Federal do Piauí)

Abstract

In this paper, we consider an abstract regularized method with a skew-symmetric mapping as regularization for solving equilibrium problems. The regularized equilibrium problem can be viewed as a generalized mixed equilibrium problem and some existence and uniqueness results are analyzed in order to study the convergence properties of the algorithm. The proposed method retrieves some existing one in the literature on equilibrium problems. We provide some numerical tests to illustrate the performance of the method. We also propose an original application to Becker's household behavior theory using the variational rationality approach of human dynamics.

Suggested Citation

  • J.X. Cruz Neto & J. O. Lopes & Antoine Soubeyran & João Carlos O. Souza, 2022. "Abstract regularized equilibria: application to Becker’s household behavior theory," Post-Print hal-03544673, HAL.
    • Handle: RePEc:hal:journl:hal-03544673
    DOI: 10.1007/s10479-021-04175-0
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03544673
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    References listed on IDEAS

    as
    1. Becker, Gary S, 1974. "A Theory of Social Interactions," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1063-1093, Nov.-Dec..
    2. G. Bento & J. Cruz Neto & G. López & Antoine Soubeyran & J. Souza, 2018. "The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem," Post-Print hal-01985333, HAL.
    3. Glaydston de C. Bento & João Xavier Cruz Neto & Lucas V. Meireles, 2018. "Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization of Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 37-52, October.
    4. Nils Langenberg, 2012. "Interior point methods for equilibrium problems," Computational Optimization and Applications, Springer, vol. 53(2), pages 453-483, October.
    5. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    6. I.V. Konnov, 2003. "Application of the Proximal Point Method to Nonmonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 317-333, November.
    7. G. C. Bento & A. Soubeyran, 2015. "Generalized Inexact Proximal Algorithms: Routine’s Formation with Resistance to Change, Following Worthwhile Changes," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 172-187, July.
    8. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.
    9. G. Bento & J. Cruz Neto & J. Lopes & A. Soares Jr & Antoine Soubeyran, 2016. "Generalized Proximal Distances for Bilevel Equilibrium Problems," Post-Print hal-01690192, HAL.
    10. Antoine Soubeyran & João Carlos O. Souza, 2020. "General descent method using w-distance. Application to emergence of habits following worthwhile moves," Post-Print hal-03135309, HAL.
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    Keywords

    Equilibrium problem; Variational rationality; Desires; Traps; Household behavior; Resource allocation problems;
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