Shapley value
A vector function defined on the set of characteristic functions of
-person games and satisfying the following axioms: 1) (efficiency) if a coalition
is such that for any coalition
the equality
holds, then
; 2) (symmetry) if
is a permutation of the set
and if for any coalition
the equality
holds, then
; and 3) (linearity)
. These axioms were introduced by L.S. Shapley [1] for an axiomatic definition of the expected pay-off in a cooperative game. It has been shown that the only vector function satisfying the axioms 1)–3) is
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References
[1] | L.S. Shapley, "A value for ![]() |
Comments
The concept of Shapley value has been modified (by several authors) by considering alternative axioms. Many applications to computations of indices of power and to various economic situations have been given. The value has also been defined for games with infinitely many players.
References
[a1] | R.J. Aumann, L.S. Shapley, "Values of non-atomic games" , Princeton Univ. Press (1974) |
[a2] | G. Owen, "Game theory" , Acad. Press (1982) |
[a3] | J.W. Friedman, "Oligopoly and the theory of games" , North-Holland (1977) |
Shapley value. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Shapley_value&oldid=32968