IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v44y2015i2p473-486.html
   My bibliography  Save this article

Stable sets in majority pillage games

Author

Listed:
  • J.S. Jordan
  • David Obadia

Abstract

A pillage game is a coalitional game in which any coalition can take all or part of the wealth of any less powerful coalition. Such an action is called pillage. In the majority pillage game, coalitional wealth contributes to coalitional power, but lexicographically less so than coalitional size. The majority pillage game refines the classic majority game in two respects. First, coalitional wealth can resolve ties in coalitional size. Second, a pillaging coalition need not contain a majority or even half of all of the players in the game. A majority of the players directly affected by the pillage, as winners or losers, is sufficient. This paper characterizes the stable sets of two and three-player games, and the symmetric (permutation invariant) stable sets of games with more than three players. For two or three players, the stable set is unique, and for any odd number of players, the symmetric stable set is unique and equal to the unique symmetric stable set for the classic majority game. If the number of players is even and at least four, no symmetric stable set exists. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • J.S. Jordan & David Obadia, 2015. "Stable sets in majority pillage games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 473-486, May.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:473-486
    DOI: 10.1007/s00182-014-0440-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-014-0440-z
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00182-014-0440-z?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. Alvin E. Roth, 1976. "Subsolutions and the Supercore of Cooperative Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 43-49, February.
    2. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590, Elsevier.
    3. Jordan, J.S., 2006. "Pillage and property," Journal of Economic Theory, Elsevier, vol. 131(1), pages 26-44, 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. Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2020. "The Last will be First, and the First Last: Segregation in Societies with Relative Payoff Concerns (RM/18/027-revised-)," Research Memorandum 011, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Talamàs, Eduard, 2018. "Fair stable sets of simple games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 574-584.
    3. Toshiji Miyakawa, 2017. "The farsighted core in a political game with asymmetric information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 205-229, June.

    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. Jung, Hanjoon Michael, 2009. "Spatial pillage game," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 701-707, December.
    2. Rowat, Colin & Kerber, Manfred, 2014. "Sufficient conditions for unique stable sets in three agent pillage games," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 69-80.
    3. Manfred Kerber & Colin Rowat, 2009. "Stable Sets in Three Agent Pillage Games," Discussion Papers 09-07, Department of Economics, University of Birmingham.
    4. Atay, Ata & Núñez, Marina, 2019. "A note on the relationship between the core and stable sets in three-sided markets," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 10-14.
    5. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    7. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.
    8. J. Jordan, 2009. "Power and efficiency in production pillage games," Review of Economic Design, Springer;Society for Economic Design, vol. 13(3), pages 171-193, September.
    9. Bhaskar Dutta & Hannu Vartiainen, 2018. "Coalition Formation and History Dependence," Working Papers 1006, Ashoka University, Department of Economics.
    10. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción, 2005. "Admissible Hierachic Sets," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    11. Inarra, Elena & Concepcion Larrea, M. & Saracho, Ana I., 2007. "The supercore for normal-form games," Journal of Economic Theory, Elsevier, vol. 132(1), pages 530-538, January.
      • Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Saracho de la Torre, Ana Isabel, 2003. "The Supercore for Normal Form Games," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    12. Jordan, J.S., 2006. "Pillage and property," Journal of Economic Theory, Elsevier, vol. 131(1), pages 26-44, November.
    13. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Saracho de la Torre, Ana Isabel, 2003. "The Supercore for Normal Form Games," IKERLANAK 2003-04, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    14. Simon MacKenzie & Manfred Kerber & Colin Rowat, 2015. "Pillage games with multiple stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 993-1013, November.
    15. Talamàs, Eduard, 2018. "Fair stable sets of simple games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 574-584.
    16. Luo, Xiao, 2001. "General systems and [phiv]-stable sets -- a formal analysis of socioeconomic environments," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 95-109, November.
    17. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción, 2005. "Admissible Hierachic Sets," IKERLANAK 2005-18, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    18. Bloch, Francis & van den Nouweland, Anne, 2020. "Farsighted stability with heterogeneous expectations," Games and Economic Behavior, Elsevier, vol. 121(C), pages 32-54.
    19. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    20. 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.

    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:jogath:v:44:y:2015:i:2:p:473-486. 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.