Equivalence of consistency and bilateral consistency through converse consistency

Theo Driessen, C.-C. Hu

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In the framework of (set-valued or single-valued) solutions for coalitional games with transferable utility, the three notions of consistency, bilateral consistency, and converse consistency are frequently used to provide axiomatic characterizations of a particular solution (like the core, prekernel, prenucleolus, Shapley value, and EANSC-value). Our main equivalence theorem claims that a solution satisfies consistency (with respect to an arbitrary reduced game) if and only if the solution satisfies both bilateral consistency and converse consistency (with respect to the same reduced game). The equivalence theorem presumes transitivity of the reduced game technique as well as difference independence on payoff vectors for two-person reduced games. Moulin's complement reduced game, Davis and Maschler's maximum reduced game and Yanovskaya and Driessen's linear reduced game versions are evaluated.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages11
Publication statusPublished - May 2006

Publication series

NameMemorandum Department of Applied Mathematics
PublisherDepartment of Applied Mathematics, University of Twente
ISSN (Print)0169-2690


  • MSC-91A12
  • EWI-8053
  • METIS-237575
  • IR-66579

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