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

Michel Grabisch and Peter Sudhölter

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Abstract: We consider TU-games with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. In such a situation, the core may be unbounded, and one has to select a bounded part of the core as a solution concept. The restricted core is obtained by imposing equality constraints in the core for sets belonging to so-called normal collections, resulting (if nonempty) in the selection of a bounded face of the core. The bounded core proves to be the union of all bounded faces (restricted cores). The paper aims at investigating in depth the relation between the bounded core and restricted cores, as well as the properties and structures of the restricted cores and normal collections. In particular, it is found that a game is convex if and only if all restricted cores corresponding to the minimal nested normal collections are nonempty. Moreover, in this case the union of these restricted cores already covers the bounded core.

Keywords: faces of the core; TU-game; restricted cooperation; distributive lattice; core; extremal rays; faces of the core.; TU; coopération restreinte; treillis distributif; coeur; rayon extrême; faces du coeur. (search for similar items in EconPapers)
Date: 2012-10
New Economics Papers: this item is included in nep-gth
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Published in 2012

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Related works:
Journal Article: 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 (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)
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