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Characterizations of solutions for games with precedence constraints

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  • Michel Grabisch

    () (University of Paris I)

  • Peter Sudhölter

    () (University of Southern Denmark)

Abstract

Abstract We generalize the characterizations of the positive core and the positive prekernel to TU games with precedence constraints and show that the positive core is characterized by non-emptiness (NE), boundedness (BOUND), covariance under strategic equivalence, closedness (CLOS), the reduced game property (RGP), the reconfirmation property (RCP) for suitably generalized Davis–Maschler reduced games, and the possibility of nondiscrimination. The bounded positive core, i.e., the union of all bounded faces of the positive core, is characterized similarly. Just RCP has to be replaced by a suitable weaker axiom, a weak version of CRGP (the converse RGP) has to be added, and CLOS can be deleted. For classical games the prenucleolus is the unique further solution that satisfies the axioms, but for games with precedence constraints it violates NE as well as the prekernel. The positive prekernel, however, is axiomatized by NE, anonymity, reasonableness, the weak RGP, CRGP, and weak unanimity for two-person games (WUTPG), and the bounded positive prekernel is axiomatized similarly by requiring WUTPG only for classical two-person games and adding BOUND.

Suggested Citation

  • Michel Grabisch & Peter Sudhölter, 2016. "Characterizations of solutions for games with precedence constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 269-290, March.
  • Handle: RePEc:spr:jogath:v:45:y:2016:i:1:d:10.1007_s00182-015-0465-y
    DOI: 10.1007/s00182-015-0465-y
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    References listed on IDEAS

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    1. Grabisch, Michel & Sudhölter, Peter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," European Journal of Operational Research, Elsevier, vol. 235(3), pages 709-717.
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    Cited by:

    1. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    2. Michel Grabisch & Peter Sudhölter, 2016. "On a class of vertices of the core," Documents de travail du Centre d'Economie de la Sorbonne 16077, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. repec:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-1057-0 is not listed on IDEAS

    More about this item

    Keywords

    TU games; Restricted cooperation; Game with precedence constraints; Positive core; Bounded core; Positive prekernel; Prenucleolus;

    JEL classification:

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

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