On the interval Shapley value

Abstract

The Shapley value is one of the most common solution concepts in Operations Research applications of cooperative game theory. It was defined and axiomatically characterized in different game-theoretic models. In this article, we focus on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real numbers. Our main contribution is to characterize the interval Shapley value by using the properties of efficiency, symmetry and strong monotonicity. We also give a characterization by using the interval dividends.

Keywords:

• cooperative games
• uncertainty
• interval data
• the Shapley value
• dividends
• Operations Research

JEL Subject Classifications:

• 91A12
• 91A40

Acknowledgements

The author gratefully acknowledges two anonymous referees.

Notes

Notes

1. Strong monotonicity property is introduced by Young 25 for the crisp case.

2. This characterization is a straightforward generalization of Young 25.

3. We follow the steps of Peters 19.

4. The definition of interval dividends is a generalization of Harsanyi 14.

5. See 10 for motivation.

6. See also 4.

7. The Moore's subtraction operator (Moore 16) is defined by .