On the core of cooperative grey games under bubbly uncertainty

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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