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The Prekernel of Cooperative Games with $$\alpha $$ α -Excess

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Listed:
  • Xia Zhang

    (NingboTech University
    Northwestern Polytechnical University
    VU University)

  • René van den Brink

    (VU University)

  • Arantza Estévez-Fernández

    (VU University)

Abstract

In this paper, we introduce a new approach to measure the dissatisfaction for coalitions of players in cooperative transferable utility games. This is done by considering affine (and convex) combinations of the classical excess and the proportional excess. Based on this so-called $$\alpha $$ α -excess, we define new solution concepts for cooperative games, such as the $$\alpha $$ α -prenucleolus and the $$\alpha $$ α -prekernel. The classical prenucleolus and prekernel are special cases. We characterize the $$\alpha $$ α -prekernel by strong stability and the $$\alpha $$ α -balanced surplus property. Also, we show that the payoff vector generated by the $$\alpha $$ α -prenucleolus belongs to the $$\alpha $$ α -prekernel.

Suggested Citation

  • Xia Zhang & René van den Brink & Arantza Estévez-Fernández, 2025. "The Prekernel of Cooperative Games with $$\alpha $$ α -Excess," Journal of Optimization Theory and Applications, Springer, vol. 206(3), pages 1-17, September.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:3:d:10.1007_s10957-025-02745-x
    DOI: 10.1007/s10957-025-02745-x
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    1. 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).
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    5. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
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