IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v59y2022i3d10.1007_s00355-022-01403-9.html
   My bibliography  Save this article

On the importance of reduced games in axiomatizing core extensions

Author

Listed:
  • Camelia Bejan

    (University of Washington, Bothell)

  • Juan Camilo Gómez

    (University of Washington, Bothell)

  • Anne van den Nouweland

    (1285 University of Oregon)

Abstract

We propose new axiomatizations of the core and three related solution concepts that also provide predictions for (classes of) games in which the core itself is empty. Our results showcase the importance of the reduced game formulation and identify the corresponding converse consistency property as the differentiating characteristic between the core and its various extensions. Existing axiomatizations of the core and similar concepts include the required form of feasibility in the generic definition of a solution concept and/or are restricted to the domain of games for which existence is guaranteed. We dispense of both practices, thus opening up the possibility of comparing, via basic axioms, solution concepts that have different feasibility constraints and domains.

Suggested Citation

  • Camelia Bejan & Juan Camilo Gómez & Anne van den Nouweland, 2022. "On the importance of reduced games in axiomatizing core extensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 637-668, October.
  • Handle: RePEc:spr:sochwe:v:59:y:2022:i:3:d:10.1007_s00355-022-01403-9
    DOI: 10.1007/s00355-022-01403-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-022-01403-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00355-022-01403-9?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. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    2. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    3. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    4. Francesc Llerena & Carles Rafels, 2007. "Convex decomposition of games and axiomatizations of the core and the D-core," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 603-615, April.
    5. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    6. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    7. Guesnerie, R. & Oddou, C., 1979. "On economic games which are not necessarily superadditive : Solution concepts and application to a local public good problem with few a agents," Economics Letters, Elsevier, vol. 3(4), pages 301-306.
    8. Peter Sudhölter & Yan-An Hwang, 2001. "Axiomatizations of the core on the universal domain and other natural domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 597-623.
    9. Bejan, Camelia & Gómez, Juan Camilo & van den Nouweland, Anne, 2021. "Feasibility-free axiomatization of the core and its non-empty extension," Economics Letters, Elsevier, vol. 201(C).
    10. Aslan, Fatma & Duman, Papatya & Trockel, Walter, 2019. "Duality for General TU-games Redefined," Center for Mathematical Economics Working Papers 620, Center for Mathematical Economics, Bielefeld University.
    11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    12. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
    13. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    14. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    15. Keiding, Hans, 1986. "An axiomatization of the core of a cooperative game," Economics Letters, Elsevier, vol. 20(2), pages 111-115.
    16. Hokari, Toru & Kibris, Ozgur, 2003. "Consistency, converse consistency, and aspirations in TU-games," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 313-331, July.
    17. Voorneveld, Mark & van den Nouweland, Anne, 1998. "A new axiomatization of the core of games with transferable utility," Economics Letters, Elsevier, vol. 60(2), pages 151-155, August.
    Full references (including those not matched with items on IDEAS)

    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. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    2. Bejan, Camelia & Gómez, Juan Camilo & van den Nouweland, Anne, 2021. "Feasibility-free axiomatization of the core and its non-empty extension," Economics Letters, Elsevier, vol. 201(C).
    3. Toru Hokari & Yukihiko Funaki & Peter Sudhölter, 2020. "Consistency, anonymity, and the core on the domain of convex games," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 187-197, December.
    4. Fatma Aslan & Papatya Duman & Walter Trockel, 2019. "Duality for General TU-games Redefined," Working Papers CIE 121, Paderborn University, CIE Center for International Economics.
    5. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2021. "Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations," Annals of Operations Research, Springer, vol. 302(1), pages 23-47, July.
    6. Sylvain Béal & Stéphane Gonzalez & Philippe Solal & Peter Sudhölter, 2023. "Axiomatic characterizations of the core without consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 687-701, September.
    7. Bas Dietzenbacher & Elena Yanovskaya, 2021. "Consistency of the equal split-off set," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 1-22, March.
    8. Pedro Calleja & Francesc Llerena, 2017. "Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 197-220, January.
    9. Pérez-Castrillo, David & Sun, Chaoran, 2021. "Value-free reductions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 543-568.
    10. Yan-An Hwang, 2013. "On the core: complement-reduced game and max-reduced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 339-355, May.
    11. Ling-Yun Chung & Yu-Hsien Liao, 2014. "A Consistent Allocation Rule: Non-emptiness, Reductions, Domination and Axiomatization," Review of Economics & Finance, Better Advances Press, Canada, vol. 4, pages 61-74, November.
    12. Bas Dietzenbacher & Peter Sudhölter, 2022. "Hart–Mas-Colell consistency and the core in convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 413-429, June.
    13. Yan-An Hwang & Yu-Hsien Liao, 2011. "The multi-core, balancedness and axiomatizations for multi-choice games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 677-689, November.
    14. Nizamogullari, Duygu & Özkal-Sanver, İpek, 2014. "Characterization of the core in full domain marriage problems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 34-42.
    15. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2019. "Cohesive efficiency in TU-games: Two extensions of the Shapley value," Working Papers 2019-03, CRESE.
    16. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    17. Yu-Hsien Liao, 2018. "The precore: converse consistent enlargements and alternative axiomatic results," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 146-163, April.
    18. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    19. Yu-Hsien Liao, 2012. "Converse consistent enlargements of the unit-level-core of the multi-choice games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 743-753, December.
    20. repec:ebl:ecbull:v:3:y:2008:i:70:p:1-8 is not listed on IDEAS
    21. Stéphane Gonzalez & Michel Grabisch, 2015. "Autonomous coalitions," Annals of Operations Research, Springer, vol. 235(1), pages 301-317, December.

    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:spr:sochwe:v:59:y:2022:i:3:d:10.1007_s00355-022-01403-9. 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.