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Department of Business and Economics, University of Southern Denmark Discussion Papers of Business and Economics
Department of Business and Economics, University of Southern Denmark

No 8/2014:
The positive core for games with precedence constraints

Michel Grabisch () and Peter Sudhölter ()

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.

Keywords: TU games; restricted cooperation; game with precedence constraints; positive core; bounded core; positive prekernel; prenucleolus; (follow links to similar papers)

JEL-Codes: C71; (follow links to similar papers)

20 pages, May 2, 2014

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