Past exam of the MSc in advanced computer science course of the University of Oxford / 2022 / Computational game theory / 4 / c / i / Solution

Yes. Use the simple cooperative game in which a coalition wins exactly when it contains at least two players. In every permutation, precisely the second arrival changes a losing coalition into a winning one. Each player is second in two of the six permutations, so each Shapley value is $2/6=1/3$. This constructs the required vector while verifying that singleton coalitions lose and the grand coalition wins.