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The quasi-prekernel for cooperative games

Author

Listed:
  • Kong, Qianqian
  • Peters, Hans
  • Sun, Hao

Abstract

The quasi-prekernel is a novel solution concept for cooperative games. It is a refinement of existing prebargaining set solutions, notably the reactive, semireactive, and Aumann-Davis-Maschler prebargaining sets. It contains the prekernel, and coincides with that solution on simple games except possibly on balanced simple games with all individual worths equal to zero. An axiomatic characterization based on reduced game properties is provided. The steady version, obtained by putting conditions on objecting and counterobjecting coalitions, is considered as well. Finally, by considering objecting and counterobjecting coalitions independent of specific players, the so-called excess prebargaining obtains, which is another novel solution concept.

Suggested Citation

  • Kong, Qianqian & Peters, Hans & Sun, Hao, 2026. "The quasi-prekernel for cooperative games," Games and Economic Behavior, Elsevier, vol. 158(C), pages 260-271.
    • Handle: RePEc:eee:gamebe:v:158:y:2026:i:c:p:260-271
    DOI: 10.1016/j.geb.2026.03.009
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    References listed on IDEAS

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    1. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
    2. Josep Izquierdo & Carles Rafels, 2012. "A characterization of convex TU games by means of the Mas-Colell bargaining set (à la Shimomura)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 381-395, May.
    3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    4. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    5. Peter Sudhölter & Jos A. M. Potters, 2001. "The semireactive bargaining set of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 117-139.
    6. Dutta, Bhaskar & Ray, Debraj & Sengupta, Kunal & Vohra, Rajiv, 1989. "A consistent bargaining set," Journal of Economic Theory, Elsevier, vol. 49(1), pages 93-112, October.
    7. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    8. Michela Chessa & Vito Fragnelli, 2014. "The bargaining set for sharing the power," Annals of Operations Research, Springer, vol. 215(1), pages 49-61, April.
    9. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    10. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
    11. Josep Maria Izquierdo & Carles Rafels, 2018. "The core and the steady bargaining set for convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 35-54, March.
    12. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    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. Robert J. Aumann, 2025. "Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 9, pages 219-242, World Scientific Publishing Co. Pte. Ltd..
    16. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    17. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 163-170, March.
    18. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    19. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    20. Alonso-Meijide, J.M. & Casas-Mendez, B. & Holler, M.J. & Lorenzo-Freire, S., 2008. "Computing power indices: Multilinear extensions and new characterizations," European Journal of Operational Research, Elsevier, vol. 188(2), pages 540-554, July.
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    JEL classification:

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

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