Overview

In this section, we mainly introduce the axiomatic properties of Shapley value. Weber et al. [17] have proved that Shapley value is the unique metric that satisfies the following axioms: Linearity, Symmetry, Dummy, and Efficiency. If two independent games u and v can be linearly merged into one game w(S) = u(S)+v(S), then the Shapley value of each player i N in the new game w is the sum of Shapley values of the player i in the game uand v, which can be formulated as: ϕw(i|N) = ϕu(i|N)+ϕv(i|N) (1) Symmetry Axiom. Considering two players i and j in a game v, if they satisfy: S N \{i,j},v(S {i}) = v(S {j}) (2) then ϕv(i|N) = ϕv(j|N). The dummy player is defined as the player that has no interaction with other players. Formally, if a player i in a game v satisfies: S N \{i},v(S {i}) = v(S)+v({i}) (3) then this player is defined as the dummy player.