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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/221763
Population Lorenz-monotonic allocation schemes for TU-games
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Sprumont (Games Econ Behav 2:378–394, 1990) introduces population monotonic allocation schemes (PMAS) and proves that every assignment game with at least two sellers and two buyers, where each buyer-seller pair derives a positive gain from trade, lacks a PMAS. In particular glove games lacks PMAS. We propose a new cooperative TU-game concept, population Lorenz-monotonic allocation schemes (PLMAS), which relaxes some population monotonicity conditions by requiring that the payoff vector of any coalition is Lorenz dominated by the corresponding restricted payoff vector of larger coalitions. We show that every TU-game having a PLMAS is totally balanced, but the converse is not true in general. We obtain a class of games having a PLMAS, but no PMAS in general. Furthermore, we prove the existence of PLMAS for every glove game and for every assignment game with at most five players.
Additionally, we also introduce two new notions, PLMAS-extendability and PLMAS-exactness, and discuss their relationships with the convexity of the game.
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IZQUIERDO AZNAR, Josep maria, MONTES, Jesús, RAFELS, Carles. Population Lorenz-monotonic allocation schemes for TU-games. _Social Choice and Welfare_. 2024. Vol. 63, núm. 2, pàgs. 417-436. [consulta: 28 de desembre de 2025]. ISSN: 0176-1714. [Disponible a: https://hdl.handle.net/2445/221763]