IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v137y2005i1p257-26810.1007-s10479-005-2260-9.html
   My bibliography  Save this article

Approximations and Well-Posedness in Multicriteria Games

Author

Listed:
  • Jacqueline Morgan

Abstract

First, sufficient conditions of minimal character are given which guarantee the sequential closedness of the set-valued function defined by the parametric weak-multicriteria Nash equilibria of a parametric multicriteria game, that is to say: a convergent sequence of parametric weak-multicriteria Nash equilibria, corresponding to an approximate value of the parameter x n , converges to a weak-multicriteria Nash equilibrium corresponding to the limit value x of the sequence (x n ) n . Then, approximating sequences and parametrically well-posedness for a multicriteria game are introduced and investigated. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:257-268:10.1007/s10479-005-2260-9
    DOI: 10.1007/s10479-005-2260-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-005-2260-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-005-2260-9?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. X. X. Huang, 2000. "Extended Well-Posedness Properties of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 165-182, July.
    2. X. X. Huang, 2001. "Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 671-684, March.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Francesco Caruso & M. Beatrice Lignola & Jacqueline Morgan, 2020. "Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 77-138, Springer.
    2. M. Chicco & F. Mignanego & L. Pusillo & S. Tijs, 2011. "Vector Optimization Problems via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 516-529, September.
    3. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    4. G. De Marco & J. Morgan, 2010. "Kalai-Smorodinsky Bargaining Solution Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 429-449, June.
    5. Giuseppe De Marco & Jacqueline Morgan, 2009. "On Multicriteria Games with Uncountable Sets of Equilibria," CSEF Working Papers 242, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    7. Giancarlo Bigi & Lorenzo Lampariello & Simone Sagratella & Valerio Giuseppe Sasso, 2023. "Approximate variational inequalities and equilibria," Computational Management Science, Springer, vol. 20(1), pages 1-16, December.
    8. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.
    9. J. W. Peng & S. Y. Wu, 2011. "The Well-Posedness for Multiobjective Generalized Games," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 416-423, August.
    10. Lucia Pusillo, 2017. "Vector Games with Potential Function," Games, MDPI, vol. 8(4), pages 1-11, September.

    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. X. J. Long & J. W. Peng, 2013. "Generalized B-Well-Posedness for Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 612-623, June.
    2. Rocca Matteo & Papalia Melania, 2008. "Well-posedness in vector optimization and scalarization results," Economics and Quantitative Methods qf0807, Department of Economics, University of Insubria.
    3. Y. P. Fang & R. Hu & N. J. Huang, 2007. "Extended B-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 445-458, December.
    4. Onetti Alberto & Verma Sameer, 2008. "Licensing and Business Models," Economics and Quantitative Methods qf0806, Department of Economics, University of Insubria.
    5. S. Li & W. Zhang, 2010. "Hadamard well-posed vector optimization problems," Journal of Global Optimization, Springer, vol. 46(3), pages 383-393, March.
    6. Miglierina Enrico & Molho Elena & Rocca Matteo, 2004. "Well-posedness and scalarization in vector optimization," Economics and Quantitative Methods qf0403, Department of Economics, University of Insubria.
    7. M. Quant & P. Borm & G. Fiestras-Janeiro & F. Megen, 2009. "On Properness and Protectiveness in Two-Person Multicriteria Games," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 499-512, March.
    8. 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.
    9. Leoneti, Alexandre Bevilacqua & Gomes, Luiz Flavio Autran Monteiro, 2021. "Modeling multicriteria group decision making as games from enhanced pairwise comparisons," Operations Research Perspectives, Elsevier, vol. 8(C).
    10. Peter Borm & Freek van Megen & Stef Tijs, 1999. "A perfectness concept for multicriteria games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 401-412, July.
    11. Anna Rettieva, 2018. "Dynamic Multicriteria Games with Finite Horizon," Mathematics, MDPI, vol. 6(9), pages 1-9, September.
    12. 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.
    13. S. Khoshkhabar-amiranloo & E. Khorram, 2015. "Pointwise well-posedness and scalarization in set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 195-210, October.
    14. Borm, Peter & Vermeulen, Dries & Voorneveld, Mark, 2003. "The structure of the set of equilibria for two person multicriteria games," European Journal of Operational Research, Elsevier, vol. 148(3), pages 480-493, August.
    15. Zachary Feinstein & Birgit Rudloff, 2021. "Characterizing and Computing the Set of Nash Equilibria via Vector Optimization," Papers 2109.14932, arXiv.org, revised Dec 2022.
    16. M. Durea, 2007. "Scalarization for pointwise well-posed vectorial problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 409-418, December.
    17. Voorneveld, Mark & Vermeulen, Dries & Borm, Peter, 1999. "Axiomatizations of Pareto Equilibria in Multicriteria Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 146-154, July.
    18. Anna N. Rettieva, 2020. "Cooperation in dynamic multicriteria games with random horizons," Journal of Global Optimization, Springer, vol. 76(3), pages 455-470, March.
    19. Kuzyutin, Denis & Smirnova, Nadezhda, 2023. "A dynamic multicriteria game of renewable resource extraction with environmentally concerned players," Economics Letters, Elsevier, vol. 226(C).
    20. Anna N. Rettieva, 2022. "Dynamic multicriteria games with asymmetric players," Journal of Global Optimization, Springer, vol. 83(3), pages 521-537, July.

    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:annopr:v:137:y:2005:i:1:p:257-268:10.1007/s10479-005-2260-9. 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.