Question: Two players i and j are substitutes in a game (N, w) if their contributions to all coalitions are identical, that is, if W(S

Two players i and j are substitutes in a game (N, w) if their contributions to all coalitions are identical, that is, if
W(S ∪ {i}) = w(S ∪ {j} for every S ⊆ N \ {i, j}
Verify that the Shapley value treats substitutes symmetrically, that is i j substitutes ⇒ ϕiw = ϕjw

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