87 Hierarchical Outcomes and Collusion Neutrality
- Biung-Ghi Ju, Junghum Park
- no.87.pdf
Abstract
We consider collusive agreements in (superadditive TU-)games that
bind collusion members to act as a single player in such a way that
the collusion performs its role in the original game if all members are
together; otherwise, the collusion plays no role, acting like the empty
set. Collusive agreements are feasible only for a set of players who
are connected on a tree. Collusion neutrality requires that no feasible
collusive agreement in
uences the total payo for the collusion mem-
bers. On the domain of all games, tree-restricted or unrestricted, there
is a solution satisfying collusion neutrality, eciency and null-player
property if and only if the tree is a line. Either replacing null-player
property with very-null-player property or restricting the domain to
the subdomain of tree-restricted games, we show that ane combina-
tions of hierarchical solutions (Demange 2004, van den Brink 2012) are
the only solutions satisfying the three axioms together with linearity.
All these results hold replacing collusion neutrality with the combi-
nation of pairwise neutrality and non-bossiness. Adding a mild equal
treatment axiom, we obtain characterizations of the average tree solu-
tion (the average of hierarchical solutions, i.e., the ane combination
with equal weights).
Keywords: Hierarchical outcomes, Collusion neutrality, TU-game, Efficiency, Null-player property, Tree, Network
JEL classification: C71