Axiomatizations of the Shapley value for cooperative games on antimatroids

E. Algaba, J. M. Bilbao, Rene van den Brink () and A. Jiménez-Losada

Mathematical Methods of Operations Research, 2003, vol. 57, issue 1, 49-65

Abstract: Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the rectricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Shapley value on antimatroids by conditions on the cooperative game v and the structure determined by the antimatroid. This axiomatization generalizes the axiomatizations of both the conjunctive and disjunctive permission value for games with a permission structure. We also provide an axiomatization of the Shapley value restricted to the smaller class of poset antimatroids. Finally, we apply our model to auction situations. Copyright Springer-Verlag Berlin Heidelberg 2003

Keywords: Mathematics Subject Classification 2000: 91A12; Key words: antimatroid; cooperative game; permission structure; Shapley value (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (27)

Downloads: (external link)
http://hdl.handle.net/10.1007/s001860200250 (text/html)
Access to full text is restricted to subscribers.

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:spr:mathme:v:57:y:2003:i:1:p:49-65

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s001860200250

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().