IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/659814.html
   My bibliography  Save this article

The Burkill-Cesari Integral on Spaces of Absolutely Continuous Games

Author

Listed:
  • F. Centrone
  • A. Martellotti

Abstract

We prove that the Burkill-Cesari integral is a value on a subspace of and then discuss its continuity with respect to both the and the Lipschitz norm. We provide an example of value on a subspace of strictly containing as well as an existence result of a Lipschitz continuous value, different from Aumann and Shapley’s one, on a subspace of .

Suggested Citation

  • F. Centrone & A. Martellotti, 2014. "The Burkill-Cesari Integral on Spaces of Absolutely Continuous Games," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:jijmms:659814
    DOI: 10.1155/2014/659814
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJMMS/2014/659814.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJMMS/2014/659814.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/659814?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
    ---><---

    References listed on IDEAS

    as
    1. Pradeep Dubey & Abraham Neyman & Robert James Weber, 1981. "Value Theory Without Efficiency," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 122-128, February.
    2. MERTENS, Jean-François, 1980. "Values and derivatives," LIDAM Reprints CORE 435, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Dov Monderer, 1990. "A Milnor Condition for Nonatomic Lipschitz Games and Its Applications," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 714-723, November.
    4. Epstein, Larry G. & Marinacci, Massimo, 2001. "The Core of Large Differentiable TU Games," Journal of Economic Theory, Elsevier, vol. 100(2), pages 235-273, October.
    5. Luigi Montrucchio & Patrizia Semeraro, 2008. "Refinement Derivatives and Values of Games," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 97-118, February.
    6. Sergiu Hart & Dov Monderer, 1997. "Potentials and Weighted Values of Nonatomic Games," Mathematics of Operations Research, INFORMS, vol. 22(3), pages 619-630, August.
    7. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
    8. Jean-François Mertens, 1980. "Values and Derivatives," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 523-552, November.
    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. F. Centrone & A. Martellotti, 2014. "Some Condition for Scalar and Vector Measure Games to Be Lipschitz," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-10, October.

    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. Luigi Montrucchio & Patrizia Semeraro, 2008. "Refinement Derivatives and Values of Games," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 97-118, February.
    2. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 313-349, June.
    3. Amarante, Massimiliano, 2014. "A characterization of exact non-atomic market games," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 59-62.
    4. M. Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2006. "Cores of non-atomic market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 399-424, October.
    5. Ori Haimanko, 2019. "The Banzhaf Value and General Semivalues for Differentiable Mixed Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 767-782, August.
    6. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    7. Mertens, J. F., 2003. "The limit-price mechanism," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 433-528, July.
    8. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    9. Epstein, Larry G. & Marinacci, Massimo, 2001. "The Core of Large Differentiable TU Games," Journal of Economic Theory, Elsevier, vol. 100(2), pages 235-273, October.
    10. Einy, Ezra & Shitovitz, Benyamin, 1999. "Fine value allocations in large exchange economies with differential information," UC3M Working papers. Economics 6128, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Other publications TiSEM 2c502ef8-76f0-47f5-ab45-1, Tilburg University, School of Economics and Management.
    12. Larry G. Epstein & Massimo Marinacci, 2000. "The Core of Large TU Games," RCER Working Papers 469, University of Rochester - Center for Economic Research (RCER).
    13. 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.
    14. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    15. Amarante, Massimiliano & Ghossoub, Mario & Phelps, Edmund, 2015. "Ambiguity on the insurer’s side: The demand for insurance," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 61-78.
    16. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January.
    17. Giulia Cesari & Roberto Lucchetti & Stefano Moretti, 2017. "Generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 919-939, November.
    18. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2004. "Voluntary formation of communities for the provision of public projects," Journal of Economic Theory, Elsevier, vol. 115(1), pages 1-34, March.
    19. Saari, Donald G. & Sieberg, Katri K., 2001. "Some Surprising Properties of Power Indices," Games and Economic Behavior, Elsevier, vol. 36(2), pages 241-263, August.
    20. Rebille, Yann, 2007. "Patience in some non-additive models," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 749-763, August.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jijmms:659814. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.