EconPapers    
Economics at your fingertips  
 

Comparable Characterizations of Four Solutions for Permission Tree Games

Rene van den Brink (jrbrink@feweb.vu.nl), Chris Dietz, Gerard van der Laan and Genjiu Xu
Additional contact information
Chris Dietz: VU University Amsterdam
Genjiu Xu: Northwestern Polytechnical University, Xi'an, Shaanxi, P.R. China

No 15-021/II, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: There is an extensive literature that studies situations of restricted cooperation in cooperative games. Myerson (1979) introduced communication graph games, where players can only cooperate if they are connected in an undirected graph representing the communication possibilities. The Myerson value is obtained by taking the Shapley value of the corresponding restricted game. For cycle-free connected graphs, Demange (2004) introduced for each player the corresponding hierarchical outcome, being the marginal contribution vector for a particular permutation of the player set induced by the graph. Gilles, Owen and van den Brink (1992) introduced games with a (hierarchical) permission structure modeled by a directed graph on the set of players. In the conjunctive (disjunctive) approach, a coalition is said to be feasible, if for every player in the coalition also all (at least one of) its predecessors (if any) belong(s) to the coalition. The conjunctive (disjunctive) permission value is obtained by taking the Shapley value of the associated conjunctive (disjunctive) restricted game. The two approaches coincide when the permission structure is a rooted tree. In this paper we consider games with a hierarchical permission structure given by a rooted tree and modify the Myerson value to a value for such games. We also consider for these games the hierarchical outcome with respect to the root of the tree (top player), along with a new solution that assigns all payoff to the unique top player in the hierarchy. Then comparable characterizations are given of these three solutions and the (conjunctive) permission value.

Keywords: Cooperative TU-game; rooted tree; Myerson value; hierarchical outcome; permission value; axiomatization (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2015-02-10
New Economics Papers: this item is included in nep-gth and nep-hpe
References: Add references at CitEc
Citations:

Downloads: (external link)
https://papers.tinbergen.nl/15021.pdf (application/pdf)

Related works:
Journal Article: Comparable characterizations of four solutions for permission tree games (2017) Downloads
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:tin:wpaper:20150021

Access Statistics for this paper

More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC.
Bibliographic data for series maintained by Tinbergen Office +31 (0)10-4088900 (discussionpapers@tinbergen.nl).

 
Page updated 2024-12-29
Handle: RePEc:tin:wpaper:20150021