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Properties of Solutions for Games on Union-Closed Systems

Author

Listed:
  • Rene van den Brink

    (School of Business and Economics, Vrije University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
    Tinbergen Institute, Gustav Mahlerplein 117, 1082 MS Amsterdam, The Netherlands)

  • Ilya Katsev

    (Yandex, Yerevan 0014, Armenia)

  • Gerard van der Laan

    (School of Business and Economics, Vrije University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
    Tinbergen Institute, Gustav Mahlerplein 117, 1082 MS Amsterdam, The Netherlands)

Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature, various models of games with restricted cooperation can be found where, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N . In this paper, we consider games on a union-closed system where the set of feasible coalitions is closed under the union, i.e., for any two feasible coalitions also, their union is feasible. Properties of solutions (the core, the nucleolus, and the prekernel) are discussed for games on a union-closed system.

Suggested Citation

  • Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:980-:d:1068341
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    References listed on IDEAS

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