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Characterization of TU games with stable cores by nested balancedness

Abstract : A balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T) to any feasible T that is not contained in S. It turns out that outvoting is transitive and the set M of maximal elements with respect to outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a super-stable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core super-stability is equivalent to vital extendability, requiring that each vital coalition is extendable.
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https://halshs.archives-ouvertes.fr/halshs-02900564
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Submitted on : Thursday, July 16, 2020 - 11:22:13 AM
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Michel Grabisch, Peter Sudhölter. Characterization of TU games with stable cores by nested balancedness. 2020. ⟨halshs-02900564⟩

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