IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v12y2010i04ns0219198910002751.html
   My bibliography  Save this article

Non-Cooperative And Axiomatic Characterizations Of The Average Lexicographic Value

Author

Listed:
  • TAKUMI KONGO

    (Faculty of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan)

  • YUKIHIKO FUNAKI

    (Faculty of Political Science and Economics, Waseda University, Japan)

  • RODICA BRANZEI

    (Faculty of Computer Science, "Alexandru Ioan Cuza" University, Iasi, Romania)

  • STEF TIJS

    (Center for Economic Research and Department of Econometrics and Operations Research, Tilburg University, The Netherlands)

Abstract

We give a non-cooperative and an axiomatic characterization of the Average Lexicographic value (AL-value) on the class of balanced games. The AL-value is a single-valued solution for balanced TU-games. It is defined as the average of lexicographic maximum of the core of the game with respect to all orders on the player set, and it can be seen as a core selection based on the priority orders on the players. In both of our characterizations of the AL-value, a consistency property which we call average consistency plays an important role, and the property is obtained by the consistency property à la Davis and Maschler of the lexicographic vectors with respect to any order of players.

Suggested Citation

  • Takumi Kongo & Yukihiko Funaki & Rodica Branzei & Stef Tijs, 2010. "Non-Cooperative And Axiomatic Characterizations Of The Average Lexicographic Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 417-435.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002751
    DOI: 10.1142/S0219198910002751
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198910002751
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198910002751?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. Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Discussion Paper 2005-123, Tilburg University, Center for Economic Research.
    2. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, November.
    3. Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Other publications TiSEM 0b4f9565-59f7-477f-b8f8-9, Tilburg University, School of Economics and Management.
    4. Caprari, E. & Tijs, S.H. & Torre, A., 2008. "Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games," Other publications TiSEM 71235183-d284-48b9-84da-c, Tilburg University, School of Economics and Management.
    5. Caprari, E. & Tijs, S.H. & Torre, A., 2008. "Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games," Discussion Paper 2008-8, Tilburg University, Center for Economic Research.
    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. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    2. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.

    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. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
    2. Grabisch, Michel & Sudhölter, Peter, 2018. "On a class of vertices of the core," Games and Economic Behavior, Elsevier, vol. 108(C), pages 541-557.
    3. Funaki, Y. & Tijs, S.H. & Brânzei, R., 2007. "Leximals, the Lexicore and the Average Lexicographic Value," Other publications TiSEM 405775ae-c634-49c5-9f9c-4, Tilburg University, School of Economics and Management.
    4. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    5. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    6. Juan Aparicio & Natividad Llorca & Joaquin Sanchez-Soriano & Manuel A. Pulido & Julia Sancho, 2012. "Ranking Auctions: A Cooperative Approach," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-19.
    7. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
    8. Louis de Mesnard, 2015. "The three wives problem and Shapley value," Post-Print hal-01091714, HAL.
    9. Vito Fragnelli & Lucia Pusillo, 2020. "Multiobjective Games for Detecting Abnormally Expressed Genes," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    10. Elisa Caprari & Fioravante Patrone & Lucia Pusillo & Stef Tijs & Anna Torre, 2008. "Share Opportunity Sets And Cooperative Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 205-218.
    11. Lohmann, E.R.M.A. & Borm, P.E.M. & Quant, M., 2007. "A Stroll with Alexia," Discussion Paper 2007-52, Tilburg University, Center for Economic Research.
    12. Lukáš Adam & Tomáš Kroupa, 2017. "The intermediate set and limiting superdifferential for coalitional games: between the core and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 891-918, November.
    13. Rene (J.R.) van den Brink & Osman Palanci & S. Zeynep Alparslan Gok, 2017. "Interval Solutions for Tu-games," Tinbergen Institute Discussion Papers 17-094/II, Tinbergen Institute.
    14. Ünsal Özdilek, 2020. "Land and building separation based on Shapley values," Palgrave Communications, Palgrave Macmillan, vol. 6(1), pages 1-13, December.
    15. Gerwald Gulick & Henk Norde, 2013. "Fuzzy cores and fuzzy balancedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 131-146, April.
    16. Barış Bülent Kırlar & Serap Ergün & Sırma Zeynep Alparslan Gök & Gerhard-Wilhelm Weber, 2018. "A game-theoretical and cryptographical approach to crypto-cloud computing and its economical and financial aspects," Annals of Operations Research, Springer, vol. 260(1), pages 217-231, January.
    17. Alparslan-Gok, S.Z. & Miquel, S. & Tijs, S.H., 2008. "Cooperation under Interval Uncertainty," Other publications TiSEM 9a01bd57-964d-4e71-8508-7, Tilburg University, School of Economics and Management.
    18. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Convex Interval Games," Other publications TiSEM d8704fc2-6edc-46cc-8330-8, Tilburg University, School of Economics and Management.
    19. Brânzei, R. & Fragnelli, V. & Meca, A. & Tijs, S.H., 2006. "Two Classes of Cooperative Games Related to One-Object Auction Situations," Discussion Paper 2006-25, Tilburg University, Center for Economic Research.
    20. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Convex Games Versus Clan Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 363-372.

    More about this item

    Keywords

    Cooperative games; average lexicographic value; average consistency; characterization; C71; C72;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002751. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.