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A Variational Approach to the Maximization of Preferences Without Numerical Representation

Author

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  • Monica Milasi

    (University of Messina)

  • Domenico Scopelliti

    (University of Messina
    University of Pavia)

Abstract

We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such conditions, we reformulate the problem as a suitable variational problem and we give regularity properties of the solutions map. The theoretical results are applied in studying an equilibrium problem under uncertainty.

Suggested Citation

  • Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
  • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01911-1
    DOI: 10.1007/s10957-021-01911-1
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    References listed on IDEAS

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    1. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    2. Giuseppe De Marco & Jacqueline Morgan, 2007. "A Refinement Concept For Equilibria In Multicriteria Games Via Stable Scalarizations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 169-181.
    3. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    4. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    5. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    6. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    7. Sophie Bade, 2005. "Nash equilibrium in games with incomplete preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 309-332, August.
    8. Patrizia Daniele & Sofia Giuffrè, 2015. "Random Variational Inequalities and the Random Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 363-381, October.
    9. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    10. Monica Milasi, 2014. "Existence theorem for a class of generalized quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 60(4), pages 679-688, December.
    11. D. Aussel & J. Cotrina, 2013. "Stability of Quasimonotone Variational Inequality Under Sign-Continuity," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 653-667, September.
    12. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    13. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
    14. Laura Scrimali & Cristina Mirabella, 2018. "Cooperation in pollution control problems via evolutionary variational inequalities," Journal of Global Optimization, Springer, vol. 70(2), pages 455-476, February.
    15. E. Allevi & A. Gnudi & I. V. Konnov & G. Oggioni, 2018. "Evaluating the effects of environmental regulations on a closed-loop supply chain network: a variational inequality approach," Annals of Operations Research, Springer, vol. 261(1), pages 1-43, February.
    16. L. S. Shapley & Fred D. Rigby, 1959. "Equilibrium points in games with vector payoffs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 6(1), pages 57-61, March.
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    Cited by:

    1. Elisabetta Allevi & Didier Aussel & Rossana Riccardi & Domenico Scopelliti, 2024. "Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 344-370, January.
    2. Orestes Bueno & John Cotrina & Yboon García, 2023. "Existence and Uniqueness of Maximal Elements for Preference Relations: Variational Approach," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1246-1263, September.
    3. Domenico Scopelliti, 2022. "On a Class of Multistage Stochastic Hierarchical Problems," Mathematics, MDPI, vol. 10(21), pages 1-13, October.

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