IDEAS home Printed from https://ideas.repec.org/p/has/discpr/2022.html
   My bibliography  Save this paper

The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games

Author

Listed:
  • P. Jean-Jacques Herings

    (Department of Economics, Maastricht University, P.O. Box 616, 6200 MD, Maastricht, The Netherlands.)

  • László Á. Kóczy

    (Institute of Economics, Centre for Economic and Regional Studies, Tóth Kálmán u. 4., 1097 Budapest, Hungary And Department of Finance, Faculty of Economics and Social Sciences, Budapest University of Technology and Economics, Magyar tudósok körútja 2, 1117 Budapest, Hungary)

Abstract

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minimal dominant set and the myopic stable set are defined by a similar set of conditions. We identify some problems with the payoff-equivalence minimal dominant set and propose an appropriate reformulation called the minimal dominant set. We show that replacing asymptotic external stability by sequential weak dominance leaves the myopic stable set unaffected. The myopic stable set is therefore equivalent to the minimal dominant set.

Suggested Citation

  • P. Jean-Jacques Herings & László Á. Kóczy, 2020. "The Equivalence of the Minimal Dominant Set and the Myopic Stable Set for Coalition Function Form Games," CERS-IE WORKING PAPERS 2022, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:2022
    as

    Download full text from publisher

    File URL: https://www.mtakti.hu/wp-content/uploads/2020/05/CERSIEWP202022.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2013. "An optimal bound to access the core in TU-games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 1-9.
    2. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
    3. Koczy, Laszlo A. & Lauwers, Luc, 2007. "The minimal dominant set is a non-empty core-extension," Games and Economic Behavior, Elsevier, vol. 61(2), pages 277-298, November.
    4. Sengupta, Abhijit & Sengupta, Kunal, 1994. "Viable Proposals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 347-359, May.
    5. Thomas Demuynck & P. Jean‐Jacques Herings & Riccardo D. Saulle & Christian Seel, 2019. "The Myopic Stable Set for Social Environments," Econometrica, Econometric Society, vol. 87(1), pages 111-138, January.
    6. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    7. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
    8. Chen, Bo & Fujishige, Satoru & Yang, Zaifu, 2016. "Random decentralized market processes for stable job matchings with competitive salaries," Journal of Economic Theory, Elsevier, vol. 165(C), pages 25-36.
    9. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
    10. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "On the number of blocks required to access the core," MPRA Paper 26578, University Library of Munich, Germany.
    11. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    12. Edward W. Packel, 1981. "A Stochastic Solution Concept for n -Person Games," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 349-362, August.
    13. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    14. Bhattacharya, Anindya & Ziad, Abderrahmane, 2006. "The core as the set of eventually stable outcomes: A note," Games and Economic Behavior, Elsevier, vol. 54(1), pages 25-30, January.
    15. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    16. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    17. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    18. Abderrahmane Ziad & Anindya Bhattacharya, 2006. "The Core as the Set of Eventually Stable Outcomes," Post-Print halshs-00078448, HAL.
    19. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    20. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    21. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    22. Bo Chen & Satoru Fujishige & Zaifu Yang, 2010. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," KIER Working Papers 749, Kyoto University, Institute of Economic Research.
    23. Jean-Jacques HERINGS & Ana MAULEON & Vincent VANNETELBOSCH, 2017. "Stable sets in matching problems with coalitional sovereignty path dominance," LIDAM Reprints CORE 2861, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    25. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    26. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    27. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    28. Yi-You Yang, 0. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 0, pages 1-17.
    29. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    30. Neuefeind, Wilhelm, 1974. "A stochastic bargaining process for n-person games," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 175-191, August.
    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. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.

    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. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    2. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.
    3. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    4. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    5. Péter Szikora, 2013. "Introduction into the literature of cooperative game theory with special emphasis on dynamic games and the core," Proceedings- 11th International Conference on Mangement, Enterprise and Benchmarking (MEB 2013),, Óbuda University, Keleti Faculty of Business and Management.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    7. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    8. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    9. Yang, Yi-You, 2012. "On the accessibility of core-extensions," Games and Economic Behavior, Elsevier, vol. 74(2), pages 687-698.
    10. Péter Szikora, 2010. "A comparison of dynamic cooperative models of coalition formation," Proceedings-8th International Conference on Mangement,Enterprise and Benchmarking (MEB 2010),, Óbuda University, Keleti Faculty of Business and Management.
    11. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2011. "On the number of blocks required to access the coalition structure core," MPRA Paper 29755, University Library of Munich, Germany.
    12. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    13. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    14. Satoru Fujishige & Zaifu Yang, 2017. "On a spontaneous decentralized market process," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 2(1), pages 1-37, December.
    15. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    16. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    17. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.
    19. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2013. "An optimal bound to access the core in TU-games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 1-9.
    20. Péter Szikora, 2012. "Dynamic cooperative models of coalition formation and the core," Proceedings- 10th International Conference on Mangement, Enterprise and Benchmarking (MEB 2012),, Óbuda University, Keleti Faculty of Business and Management.

    More about this item

    Keywords

    coalition structure core; sequential dominance;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:has:discpr:2022. 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: Nora Horvath (email available below). General contact details of provider: https://edirc.repec.org/data/iehashu.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.