Characterization of TU games with stable cores by nested balancedness

Michel Grabisch and Peter Sudhölter

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) 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)
Date: 2024
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Published in Mathematical Programming, 2024, 203, pp.801-826. ⟨10.1007/s10107-021-01716-0⟩

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Related works:
Working Paper: Characterization of TU games with stable cores by nested balancedness (2024)
Working Paper: Characterization of TU games with stable cores by nested balancedness (2024)
Working Paper: Characterization of TU games with stable cores by nested balancedness (2020)
Working Paper: Characterization of TU games with stable cores by nested balancedness (2020)
Working Paper: Characterization of TU games with stable cores by nested balancedness (2020)
Working Paper: Characterization of TU games with stable cores by nested balancedness (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-03881408

DOI: 10.1007/s10107-021-01716-0

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