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Extendable Cooperative Games
Author(s) -
AZRIELI YARON,
LEHRER EHUD
Publication year - 2007
Publication title -
journal of public economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.809
H-Index - 32
eISSN - 1467-9779
pISSN - 1097-3923
DOI - 10.1111/j.1467-9779.2007.00345.x
Subject(s) - core (optical fiber) , extension (predicate logic) , subgame perfect equilibrium , mathematical economics , cover (algebra) , computer science , mathematics , game theory , engineering , programming language , telecommunications , mechanical engineering
A (TU) cooperative game is extendable if every core allocation of each subgame can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its subgames can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core. Further, we characterize extendability in terms of an extension of the balanced cover of the game. It is also shown how this extension can unify the analysis of many families of games under one roof.