Cooperative grey games and the grey Shapley value

• Published in: Optimization Vol. 64; no. 8; pp. 1657 - 1668
• Main Authors: Palancı, O., Alparslan Gök, S.Z., Ergün, S., Weber, G.-W.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03-08-2015; Taylor & Francis LLC
• Subjects: cooperative games; Dummies; Economics; Game theory; interval grey numbers; Mathematical analysis; Operational research; Operations research; Optimization; Players; Shapley value; Studies; Symmetry; uncertainty
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2014.956743

This contribution is located in the common area of operational research and economics, with a close relation and joint future potential with optimization: game theory. We focus on collaborative game theory under uncertainty. This study is on a new class of cooperative games where the set of players is finite and the coalition values are interval grey numbers. An interesting solution concept, the grey Shapley value, is introduced and characterized with the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. The paper ends with a conclusion and an outlook to future studies.