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Monotonicity and weighted prenucleoli: A characterization without consistency

Pedro Calleja (), Francesc Llerena () and Peter Sudhölter ()
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Pedro Calleja: Departament de Matematica Economica, Financera i Actuarial, Postal: BEAT, University of Barcelona, 08034 Barcelona, Spain
Francesc Llerena: Departament de Gestió d'Empreses, Postal: CREIP, Universitat Rovira i Virgili, 43204 Reus, Spain

Authors registered in the RePEc Author Service: Francesc Llerena Garrés

No 4/2018, Discussion Papers of Business and Economics from University of Southern Denmark, Department of Business and Economics

Abstract: 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 and scale covariance (COV), and equal adjusted surplus division (EASD), a property that is comparable 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)Sp. We show that the p-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, COV, and IASp; and on larger sets by additionally requiring ISp.

Keywords: TU games; weighted prenucleolus; equal surplus division (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-upt
Date: 2018-05-17
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Handle: RePEc:hhs:sdueko:2018_004