IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v10y2008i04ns0219198908001996.html
   My bibliography  Save this article

Convex Games Versus Clan Games

Author

Listed:
  • RODICA BRANZEI

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

  • DINKO DIMITROV

    (Chair of Microeconomics, Faculty of Law and Economics, University of Bayreuth, Germany)

  • STEF TIJS

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

Abstract

In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games. Furthermore, each monotonic convex game generates a total clan game with zero worth for the clan by a "dualize and extend" procedure. These procedures are also useful for relating core elements and elements of the Weber set of the corresponding games.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:n:s0219198908001996
    DOI: 10.1142/S0219198908001996
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198908001996
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198908001996?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Tijs, S.H. & Meca, A. & Lopez, M.A., 2005. "Benefit sharing in holding situations," Other publications TiSEM 718b8e18-eb6f-407b-a9cd-e, Tilburg University, School of Economics and Management.
    2. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    3. Brânzei, R. & Fragnelli, V. & Meca, A. & Tijs, S.H., 2006. "Two Classes of Cooperative Games Related to One-Object Auction Situations," Other publications TiSEM 67acfa22-d353-4af6-b913-1, Tilburg University, School of Economics and Management.
    4. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "The Equal Split-Off Set for Cooperative Games," Other publications TiSEM d83ae0df-8e70-4427-a46a-2, Tilburg University, School of Economics and Management.
    5. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, October.
    6. Antonio Caparrós Ruiz & Mª. Lucía Navarro Gómez, 2002. "Factors affecting quits and layoffs in Spain," Economic Working Papers at Centro de Estudios Andaluces E2002/16, Centro de Estudios Andaluces.
    7. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    8. Tijs, Stef & Meca, Ana & Lopez, Marco A., 2005. "Benefit sharing in holding situations," European Journal of Operational Research, Elsevier, vol. 162(1), pages 251-269, April.
    9. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    10. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
    11. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "A New Characterization of Convex Games," Other publications TiSEM 34e9abd5-a96f-47e4-b313-d, Tilburg University, School of Economics and Management.
    12. Curiel, I. & Tijs, S.H., 1991. "Minimarg and the maximarg operators," Other publications TiSEM 1f024ef6-4383-41ae-aba6-0, Tilburg University, School of Economics and Management.
    13. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    14. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2001. "Information collecting situations and bi-monotonic allocation schemes," Other publications TiSEM b1fe5187-5a46-460d-aaeb-9, Tilburg University, School of Economics and Management.
    15. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
    16. Rodica Brânzei & Stef Tijs & Judith Timmer, 2001. "Information collecting situations and bi-monotonic allocation schemes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 303-313, December.
    17. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    18. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    19. Juan Enrique Martínez-Legaz, 2006. "Some Characterizations of Convex Games," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 293-303, Springer.
    20. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, University Library of Munich, Germany.
    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. Béal, Sylvain & Durieu, Jacques & Solal, Philippe, 2008. "Farsighted coalitional stability in TU-games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 303-313, November.
    2. Brânzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Discussion Paper 2008-55, Tilburg University, Center for Economic Research.
    3. Brânzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Other publications TiSEM bfc414e8-1720-4cfd-a0ac-f, Tilburg University, School of Economics and Management.
    4. Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December.

    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. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2011. "Convex games, clan games, and their marginal games," Center for Mathematical Economics Working Papers 368, Center for Mathematical Economics, Bielefeld University.
    2. Brânzei, R. & Solymosi, T. & Tijs, S.H., 2003. "Type Monotonic Allocation Schemes for Multi-Glove Games," Other publications TiSEM 2fed3103-b346-4023-a36d-f, Tilburg University, School of Economics and Management.
    3. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Multi-Choice Total Clan Games : Characterizations and Solution Concepts," Discussion Paper 2007-77, Tilburg University, Center for Economic Research.
    4. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    5. R. Branzei & N. Llorca & J. Sánchez-Soriano & S. Tijs, 2009. "Multi-choice clan games and their core," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 123-138, July.
    6. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Other publications TiSEM 5549df35-acc3-4890-be43-4, Tilburg University, School of Economics and Management.
    7. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Discussion Paper 2007-54, Tilburg University, Center for Economic Research.
    8. Platz, T.T. & Hamers, H.J.M. & Quant, M., 2011. "Characterizing Compromise Stability of Games Using Larginal Vectors," Discussion Paper 2011-058, Tilburg University, Center for Economic Research.
    9. 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.
    10. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & van Velzen, S., 2003. "Compromise Stable TU-Games," Discussion Paper 2003-55, Tilburg University, Center for Economic Research.
    11. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    12. Alparslan Gök, S.Z. & Özcan, İ., 2023. "On big boss fuzzy interval games," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1040-1046.
    13. Tijs, S.H. & Brânzei, R. & Muto, S. & Ishihara, S. & Fukuda, E., 2002. "Fuzzy Clan Games and Bi-monotonic Allocation Rules," Other publications TiSEM b5200e92-83d8-4fd9-b7f2-9, Tilburg University, School of Economics and Management.
    14. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Multi-Choice Total Clan Games : Characterizations and Solution Concepts," Other publications TiSEM 31aee267-f432-46c8-b078-1, Tilburg University, School of Economics and Management.
    15. Mark Voorneveld & Stef Tijs & Sofia Grahn, 2003. "Monotonic allocation schemes in clan games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(3), pages 439-449, January.
    16. Josep Maria Izquierdo Aznar, 2003. "Regular Population Monotonic Allocation Schemes and the Core," Working Papers in Economics 110, Universitat de Barcelona. Espai de Recerca en Economia.
    17. Tijs, S.H. & Moretti, S. & Brânzei, R. & Norde, H.W., 2005. "The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects," Discussion Paper 2005-3, Tilburg University, Center for Economic Research.
    18. Saadia Obadi & Silvia Miquel, 2017. "Clan information market games," Theory and Decision, Springer, vol. 82(4), pages 501-517, April.
    19. Trine Platz & Herbert Hamers & Marieke Quant, 2014. "C-complete sets for compromise stable games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 213-223, October.
    20. Tijs, S.H. & Brânzei, R. & Muto, S. & Ishihara, S. & Fukuda, E., 2002. "Fuzzy Clan Games and Bi-monotonic Allocation Rules," Discussion Paper 2002-115, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    Convex games; core; dual games; marginal games; total clan games; Weber set; C71;
    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:10:y:2008:i:04:n:s0219198908001996. 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.