Interaction indices for games on combinatorial structures with forbidden coalitions

Christophe Labreuche

European Journal of Operational Research, 2011, vol. 214, issue 1, 99-108

Abstract: The notion of interaction among a set of players has been defined on the Boolean lattice and Cartesian products of lattices. The aim of this paper is to extend this concept to combinatorial structures with forbidden coalitions. The set of feasible coalitions is supposed to fulfil some general conditions. This general representation encompasses convex geometries, antimatroids, augmenting systems and distributive lattices. Two axiomatic characterizations are obtained. They both assume that the Shapley value is already defined on the combinatorial structures. The first one is restricted to pairs of players and is based on a generalization of a recursivity axiom that uniquely specifies the interaction index from the Shapley value when all coalitions are permitted. This unique correspondence cannot be maintained when some coalitions are forbidden. From this, a weak recursivity axiom is defined. We show that this axiom together with linearity and dummy player are sufficient to specify the interaction index. The second axiomatic characterization is obtained from the linearity, dummy player and partnership axioms. An interpretation of the interaction index in the context of surplus sharing is also proposed. Finally, our interaction index is instantiated to the case of games under precedence constraints.

Keywords: Game; theory; Cooperative; games; Interaction; index; Combinatorial; structure; Shapley; value (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221711003493
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:214:y:2011:i:1:p:99-108

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().