IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v86y2023i4d10.1007_s10898-023-01282-z.html
   My bibliography  Save this article

On the study of multistage stochastic vector quasi-variational problems

Author

Listed:
  • Elena Molho

    (University of Pavia)

  • Domenico Scopelliti

    (Department of Economics and Management)

Abstract

This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields; these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem; stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinear scalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model.

Suggested Citation

  • Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:4:d:10.1007_s10898-023-01282-z
    DOI: 10.1007/s10898-023-01282-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-023-01282-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-023-01282-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    2. A. Cambini & D.T. Luc & L. Martein, 2003. "Order-Preserving Transformations and Applications," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 275-293, August.
    3. Limosani, Michele & Milasi, Monica & Scopelliti, Domenico, 2021. "Deregulated electricity market, a stochastic variational approach," Energy Economics, Elsevier, vol. 103(C).
    4. Q. H. Ansari & S. Schaible & J. C. Yao, 2000. "System of Vector Equilibrium Problems and Its Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 547-557, December.
    5. 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.
    6. Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.
    7. Georgia Fargetta & Antonino Maugeri & Laura Scrimali, 2022. "A Stochastic Nash Equilibrium Problem for Medical Supply Competition," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 354-380, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amparo M. Mármol & Luisa Monroy & M. Ángeles Caraballo & Asunción Zapata, 2017. "Equilibria with vector-valued utilities and preference information. The analysis of a mixed duopoly," Theory and Decision, Springer, vol. 83(3), pages 365-383, October.
    2. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    3. Juho Kokkala & Kimmo Berg & Kai Virtanen & Jirka Poropudas, 2019. "Rationalizable strategies in games with incomplete preferences," Theory and Decision, Springer, vol. 86(2), pages 185-204, March.
    4. Park, Jaeok, 2015. "Potential games with incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 58-66.
    5. Jaeok Park, 2019. "Decision Making and Games with Vector Outcomes," Working papers 2019rwp-146, Yonsei University, Yonsei Economics Research Institute.
    6. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    7. Domenico Scopelliti, 2022. "On a Class of Multistage Stochastic Hierarchical Problems," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    8. Yasuo Sasaki, 2019. "Rationalizability in multicriteria games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 673-685, June.
    9. 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.
    10. A. Zapata & A. M. Mármol & L. Monroy & M. A. Caraballo, 2019. "A Maxmin Approach for the Equilibria of Vector-Valued Games," Group Decision and Negotiation, Springer, vol. 28(2), pages 415-432, April.
    11. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    12. 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.
    13. Sasaki, Yasuo, 2022. "Unawareness of decision criteria in multicriteria games," Mathematical Social Sciences, Elsevier, vol. 119(C), pages 31-40.
    14. Andrew Caplin & Mark Dean & Daniel Martin, 2011. "Search and Satisficing," American Economic Review, American Economic Association, vol. 101(7), pages 2899-2922, December.
    15. Paola Manzini & Marco Mariotti, 2003. "How vague can one be? Rational preferences without completeness or transitivity," Game Theory and Information 0312006, University Library of Munich, Germany, revised 16 Jul 2004.
    16. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    17. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    18. 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.
    19. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    20. Ovidiu Bagdasar & Nicolae Popovici, 2018. "Unifying local–global type properties in vector optimization," Journal of Global Optimization, Springer, vol. 72(2), pages 155-179, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:86:y:2023:i:4:d:10.1007_s10898-023-01282-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.