A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core

Jiuqiang Liu and Xiaodong Liu

Journal of Mathematical Economics, 2013, vol. 49, issue 2, 150-156

Abstract: In 2004, Predtetchinski and Herings [A. Predtetchinski, P.J.J. Herings, “A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game”, Journal of Economic Theory 116 (2004) 84–92] provided a necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game. In this paper, we extend this theorem to its counterpart in fuzzy games and give a necessary and sufficient condition for a non-transferable utility fuzzy game to have a non-empty fuzzy core. As a consequence, we derive a necessary and sufficient condition for non-emptiness of the fuzzy core of a TU fuzzy game.

Keywords: Cores; Balanced collections; π-balanced collections; Π-balanced collections; TU games; NTU games; Fan’s Coincidence theorem; Heine–Borel finite cover theorem (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:49:y:2013:i:2:p:150-156

DOI: 10.1016/j.jmateco.2012.12.002

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