Population Lorenz-monotonic allocation schemes for TU-games

Bibliographic Data

ID21470519
AuthorsJosep M Izquierdo (0000-0003-4104-9604, Universitat de Barcelona, corresponding author), Jesús Montes, Jesús Montes Peral (0000-0002-2059-0648, Universitat Abat Oliba CEU), Carlos Rafels (0000-0001-6804-9538, Universitat de Barcelona)
Year2024
Volume63
Issue2
Pages417-436
Publication date2024-09-01
Open AccessYes
TypeARTICLE
VenueSocial Choice and Welfare (JOURNAL)
Journal identifiersISSN: 0176-1714 • E-ISSN: 1432-217X
PublisherSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s00355-024-01538-x
OpenAlexW4400677485
LanguageEN
References cited30

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

Converse · Convexity · Economics · Game theory · Mathematical economics · Mathematical optimization · Monotonic function · Population · Stochastic game · Computer Science · Economic and Environmental Valuation · Experimental Behavioral Economics Studies · Game Theory and Voting Systems · Mathematics

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