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The positive core for games with precedence constraints

Author

Listed:
  • Grabisch, Michel

    () (Paris School of Economics)

  • Sudhölter, Peter

    () (Department of Business and Economics)

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

  • Grabisch, Michel & Sudhölter, Peter, 2014. "The positive core for games with precedence constraints," Discussion Papers of Business and Economics 8/2014, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2014_008
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    References listed on IDEAS

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    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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