Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency
| Autor: | Francesc Llerena, Pedro Calleja, Peter Sudhölter |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
General Mathematics
0211 other engineering and technologies Scale (descriptive set theory) Monotonic function 02 engineering and technology Management Science and Operations Research Characterization (mathematics) Grand coalition Combinatorics Set (abstract data type) TU games Consistency (statistics) 0502 economics and business equal surplus division Transferable utility Independence (probability theory) Game theory aggregate monotonicity Mathematics Cooperative games (Mathematics) 021103 operations research weighted prenucleolus 05 social sciences Aggregate (data warehouse) Covariance Computer Science Applications Teoria de jocs Jocs cooperatius (Matemàtica) 050206 economic theory |
| Zdroj: | Dipòsit Digital de la UB Universidad de Barcelona Calleja, P, Llerena, F & Sudholter, P 2020, ' Monotonicity and Weighted Prenucleoli : A Characterization without Consistency ', Mathematics of Operations Research, vol. 45, no. 3, pp. 1056-1068 . https://doi.org/10.1287/moor.2019.1022 |
| DOI: | 10.1287/moor.2019.1022 |
| Popis: | 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)Sp. We show that the p-weighted prenucleolus on the set of balanced TU games is characterized by SIVA, TCOV, SCOV, and IASp and on larger sets by additionally requiring ISp. |
| Databáze: | OpenAIRE |
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