Unblocked Imputations of Fuzzy Games. I: Existence

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize the well-known Scarf theorem on the nonemptiness of the core to the case of generalized fuzzy cooperative games without side payments provided that the set of blocking coalitions is extended by the so-called fuzzy coalitions. The notion of a balanced family is extended to the case of an arbitrary set of fuzzy blocking coalitions, owing to which it is possible to introduce a natural analogue of balancedness of a fuzzy game for the characteristic function with an arbitrary efficiency domain. Based on an appropriate approximation of a fuzzy game by finitely-generated games, together with the seminal combinatorial Scarf lemma on ordinal and admissible bases, we obtain rather general conditions of the existence of unblocked imputations for F-balanced fuzzy cooperative games. Bibliography: 15 titles.

Original languageEnglish
Pages (from-to)828-845
Number of pages18
JournalJournal of Mathematical Sciences (United States)
Volume246
Issue number6
DOIs
Publication statusPublished - 1 May 2020

Fingerprint

Dive into the research topics of 'Unblocked Imputations of Fuzzy Games. I: Existence'. Together they form a unique fingerprint.

Cite this