Arbeitspapier
Comparable Characterizations of Four Solutions for Permission Tree Games
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.
- Sprache
-
Englisch
- Erschienen in
-
Series: Tinbergen Institute Discussion Paper ; No. 15-021/II
- Klassifikation
-
Wirtschaft
Cooperative Games
- Thema
-
Cooperative TU-game
rooted tree
Myerson value
hierarchical outcome
permission value
axiomatization
- Ereignis
-
Geistige Schöpfung
- (wer)
-
van den Brink, René
Dietz, Chris
van der Laan, Gerard
Xu, Genjiu
- Ereignis
-
Veröffentlichung
- (wer)
-
Tinbergen Institute
- (wo)
-
Amsterdam and Rotterdam
- (wann)
-
2015
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:44 MEZ
Datenpartner
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Objekttyp
- Arbeitspapier
Beteiligte
- van den Brink, René
- Dietz, Chris
- van der Laan, Gerard
- Xu, Genjiu
- Tinbergen Institute
Entstanden
- 2015
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