On the core of cooperative grey games under bubbly uncertainty

Year 2024, , 530 - 536, 31.12.2024

İsmail Özcan , Sırma Zeynep Alparslan Gök , Gerhard-wilhelm Weber

https://doi.org/10.56554/jtom.1285698

Abstract

This paper introduces a novel category of cooperative games called
cooperative bubbly grey games, in which the value of each coalition
is represented by a grey bubble rather than a numerical value. To
be exact, rather of using actual numbers, the coalition values are rep-
resented as bubbles. Accordingly, we use the cooperative grey game
model to overcome the bubbly uncertainty. Both the idea of the bub-
bly core and the cooperative bubbly game concept are introduced.
Grey data may be used as a tool in cooperative grey games to address
pro…t or cost-sharing challenges. When considering cooperative grey
bubbly games, we can take the advantage of the fact that each bubble
are characterized exactly by grey numbers where the logarithmic grey
price process is represented with bubbles. Additionally, the bubbly
core, a novel solution concept, is presented. In addition, a numerical
example is provided along with a required criterion for non-emptiness
of the bubbly grey core of such a game.

Keywords

cooperative game theory, grey numbers, uncertainty, bubble, core

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