On the restricted cores and the bounded core of games on distributive lattices

Michel Grabisch and Peter Sudhölter

European Journal of Operational Research, 2014, vol. 235, issue 3, 709-717

Abstract: A game with precedence constraints is a TU game with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. Its core may be unbounded, and the bounded core, which is the union of all bounded faces of the core, proves to be a useful solution concept in the framework of games with precedence constraints. Replacing the inequalities that define the core by equations for a collection of coalitions results in a face of the core. A collection of coalitions is called normal if its resulting face is bounded. The bounded core is the union of all faces corresponding to minimal normal collections. We show that two faces corresponding to distinct normal collections may be distinct. Moreover, we prove that for superadditive games and convex games only intersecting and nested minimal collection, respectively, are necessary. Finally, it is shown that the faces corresponding to pairwise distinct nested normal collections may be pairwise distinct, and we provide a means to generate all such collections.

Keywords: Game theory; Restricted cooperation; Distributive lattice; Core; Extremal rays; Faces of the core (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

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Related works:
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2014)
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2014)
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2014)
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2012)
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2012)
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2012)
Working Paper: On the restricted cores and the bounded core of games on distributive lattices (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:235:y:2014:i:3:p:709-717

DOI: 10.1016/j.ejor.2013.10.027

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