Variations on the Shapley value

(3) Owen (1977) and Hart and Kurz (1983) gave an axiomatic characterization
of the coalitional structure value as an operator which is defined on pairs
(v, π), using axioms that consider changes in the values of such an operator
when both the game and the partition are changed.
(4) McLean (1991) defined and analyzed coalitional structure random-order
values, as follows. Let π be a partition of N and let b ∈ ∆(OR). b is
consistent with π if b(τ) = 0 for every order τ which is not consistent with
π. A random order value is a π random order coalitional structure value if it
is defined by some b ∈ ∆(OR) which is consistent with π. Levy and McLean
(1989) defined and characterized weighted coalitional structure values.
(5) McLean and Ye (1996) developed the theory of coalitional structure semi-
values for finite games.
(6) Winter (1992) characterized the Owen value by a consistency property which
generalizes the one given in Hart and Mas-Colell (1989). He also generalized
the potential approach and showed that the Owen value, Myerson value and
A-D value can be developed through this approach.
(7) Winter (1989) developed the theory of values defined on pairs (v, p), where
v ∈ G and p = (π1, . . . , πm) is a decreasing sequence of partitions. 10
(8) Lucas (1963) and Myerson (1976) dealt with values of generalized games,
References.
where the worth of a coalition also depends on the partition into coalitions
generated by the players.
R. Amer and F. Carreras (1995). Games and Cooperation Indices. Interna-
10 The idea for dealing with such values appears in Owen (1977).
30