Cooperative grey games and the grey Shapley value

Abstract

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.

Keywords:

• cooperative games
• uncertainty
• interval grey numbers
• Shapley value
• operations research

AMS Subject Classification:

• 91A12

Notes

1 The classical Shapley value is first introduced and characterized by Shapley [29, 30], which is the most interesting one point allocation rule on the theory of cooperative games.

2 In our results, we are inspired from [31].