IDEAS home Printed from https://ideas.repec.org/p/ins/quaeco/qf0507.html
   My bibliography  Save this paper

An axiomatic approach to approximate solutions in vector optimization

Author

Listed:
  • Miglierina Enrico

    (Department of Economics, University of Insubria, Italy)

  • Molho Elena

    (Department of Management Sciences, University of Pavia)

  • Patrone Fioravante

    (Department of Mathematics, University of Genoa, Italy)

  • Steff H. Tijs

    (Department of Econometrics, University of Tilburg, Netherlands)

Abstract

In vector optimization many notions of approximate solution have been proposed in the literature. In this paper an axiomatic approach is introduced in order to study the approximate solution map of a vector optimization problem in the image space. An impossibility result is proved in the sense that, whenever all of the axioms are satisfied, either the set of the approximate solutions is a subset of the exact solution of the problem (the weakly efficient frontier), or it coincides with the whole admissible set. Moreover, the geometry of the approximate solution map is studied in the special case of polyhedral ordering cones generated by a base of R. Finally, we study the shape of the approximate solution map under the assumption of weak approximation consistency.

Suggested Citation

  • Miglierina Enrico & Molho Elena & Patrone Fioravante & Steff H. Tijs, 2005. "An axiomatic approach to approximate solutions in vector optimization," Economics and Quantitative Methods qf0507, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0507
    as

    Download full text from publisher

    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2005_10.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Graziano Pieri & Fioravante Patrone & Anna Torre & Stef Tijs, 1998. "On consistent solutions for strategic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 191-200.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Norde, Henk & Patrone, Fioravante & Tijs, Stef, 2000. "Characterizing properties of approximate solutions for optimization problems," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 297-311, November.
    4. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    5. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1998. "On consistent solutions for strategic games," Other publications TiSEM cc482511-a079-4067-88b2-0, Tilburg University, School of Economics and Management.
    6. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
    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. E. Miglierina & E. Molho & F. Patrone & S. Tijs, 2008. "Axiomatic approach to approximate solutions in multiobjective optimization," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(2), pages 95-115, November.
    2. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    3. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.
    4. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Concept of the Core of Games in Effectiveness Form," GREDEG Working Papers 2018-15, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    5. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    6. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    7. Maurizio Zanardi, 2004. "Antidumping law as a collusive device," Canadian Journal of Economics, Canadian Economics Association, vol. 37(1), pages 95-122, February.
    8. M. Hinojosa & A. Mármol & J. Zarzuelo, 2008. "Inequality averse multi-utilitarian bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 597-618, December.
    9. Matsui, Kenji, 2020. "Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain," European Journal of Operational Research, Elsevier, vol. 287(1), pages 225-236.
    10. Simon G�chter & Arno Riedl, "undated". "Moral Property Rights in Bargaining," IEW - Working Papers 113, Institute for Empirical Research in Economics - University of Zurich.
    11. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    12. Erkki Koskela & Ronnie Schöb, 2002. "Alleviating Unemployment: The Case for Green Tax Reforms," Chapters, in: Lawrence H. Goulder (ed.), Environmental Policy Making in Economies with Prior Tax Distortions, chapter 20, pages 355-378, Edward Elgar Publishing.
    13. Magni, Carlo Alberto, 2009. "Splitting up value: A critical review of residual income theories," European Journal of Operational Research, Elsevier, vol. 198(1), pages 1-22, October.
    14. Stefano Vannucci, 2015. "La teoria dei giochi e John Nash," Department of Economics University of Siena 722, Department of Economics, University of Siena.
    15. Roland Kirstein & Matthias Peiss, 2013. "Quantitative Machtkonzepte in der Ökonomik," FEMM Working Papers 130004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    16. Michael Carter & Julian Wright, 1999. "Interconnection in Network Industries," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 14(1), pages 1-25, February.
    17. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    18. Thomas M. Humphrey, 1996. "The early history of the box diagram," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 37-75.
    19. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    20. Izat B. Baybusinov & Enrico Maria Fenoaltea & Yi-Cheng Zhang, 2022. "Negotiation problem," Papers 2201.12619, arXiv.org.

    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:ins:quaeco:qf0507. 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: Segreteria Dipartimento (email available below). General contact details of provider: https://edirc.repec.org/data/feinsit.html .

    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.