 Characterization of TU games with stable cores by nested balancednessMichel Grabisch and Peter Sudhölter PSE-Ecole d'économie de Paris (Postprint) from HAL 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. Keywords: Domination; Stable set; Core; TU game (search for similar items in EconPapers) Published in Mathematical Programming, 2024, 203, pp.801-826. ⟨10.1007/s10107-021-01716-0⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-03881408 DOI: 10.1007/s10107-021-01716-0 Access Statistics for this paper More papers in PSE-Ecole d'économie de Paris (Postprint) from HAL |
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