Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency
A solution on a set of transferable utility (TU) games satisfies strong aggregate monotonicity (SAM) if every player can improve when the grand coalition becomes richer. It satisfies equal surplus division (ESD) if the solution allows the players to improve equally. We show that the set of weight sy...
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Veröffentlicht in: | Mathematics of operations research 2020-08, Vol.45 (3), p.1056-1068 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | A solution on a set of transferable utility (TU) games satisfies
strong aggregate monotonicity
(SAM) if every player can improve when the grand coalition becomes richer. It satisfies
equal surplus division
(ESD) if the solution allows the players to improve equally. We show that the set of weight systems generating weighted prenucleoli that satisfy SAM is open, which implies that for weight systems close enough to any regular system, the weighted prenucleolus satisfies SAM. We also provide a necessary condition for SAM for symmetrically weighted nucleoli. Moreover, we show that the per capita nucleolus on balanced games is characterized by
single-valuedness
(SIVA),
translation covariance
(TCOV) and
scale covariance
(SCOV), and equal
adjusted
surplus division (EASD), a property that is comparable to but stronger than ESD. These properties together with ESD characterize the per capita prenucleolus on larger sets of TU games. EASD and ESD can be transformed to
independence of
(
adjusted
)
proportional shifting
, and these properties may be generalized for arbitrary weight systems
p
to I(A)S
p
. We show that the
p
-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, TCOV, SCOV, and IAS
p
and on larger sets by additionally requiring IS
p
. |
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ISSN: | 0364-765X 1526-5471 |
DOI: | 10.1287/moor.2019.1022 |