An Alternative Approach to the Axiomatic Characterization of the Interval Shapley Value

Abstract

This study presents a new approach to the axiomatic characterization of the interval Shapley value. This approach aims to improve our comprehension of the particular characteristics of the interval Shapley value in a provided context. Furthermore, the research contributes to the related literature by expanding and applying the fundamental axiomatic principles used to define the interval Shapley value. The proposed axioms encompass symmetry, gain-loss, and differential marginality, offering a distinctive framework for understanding and characterizing the interval Shapley value. Through these axioms, the paper examines and interprets the intrinsic properties of the value objectively, presenting a new perspective on the interval Shapley value. The characterization highlights the importance and distinctiveness of the interval Shapley value.

Keywords

• Cooperative interval games
• uncertainty
• interval Shapley value
• axiomatic characterization

References

1. L. S. Shapley, A value for $n$-person games, Annals of Mathematics Studies 28 (1953) 307-317.
2. P. Borm, H. Hamers, R. Hendrickx, Operations research games: A survey, Top 9 (2) (2001) 139-216.
3. Y. Chun, On the symmetric and weighted Shapley values, International Journal of Game Theory 20 (2) (1991) 183-190.
4. S. Z. Alparslan Gök, R. Branzei, S. Tijs, The interval Shapley value: An axiomatization, Central European Journal of Operations Research 18 (2) (2010) 131-140.
5. S. Z. Alparslan Gök, On the interval Shapley value, Optimization 63 (5) (2014) 747-755.
6. M. Ekici, O. Palanci, S. Z. Alparslan Gök, The grey Shapley value: An axiomatization, in: H. Mawengkang (Ed.), 4th International Conference on Operational Research (InteriOR), Medan, 2018, 012082 7 pages.
7. U. A. Yılmaz, S. Z. Alparslan Gök, M. Ekici, O. Palanci, On the grey equal surplus sharing solutions, International Journal of Supply and Operations Management 5 (1) (2018) 1-10.
8. H. P. Young, Monotonic solutions of cooperative games, International Journal of Game Theory 14 (2) (1985) 65-72.

9. R. van den Brink, An axiomatization of the Shapley value using a fairness property, International Journal of Game Theory 30 (3) (2002) 309-319.
10. Y. Chun, A new axiomatization of the Shapley value, Games and Economic Behavior 1 (2) (1989) 119-130.
11. A. Casajus, Differential marginality, van den Brink fairness, and the Shapley value, Theory and Decision 71 (2) (2011) 163-174.
12. E. Shan, Z. Cui, W. Lyu, Gain–loss and new axiomatizations of the Shapley value, Economics Letters 228 (2023) 111168 4 pages.
13. O. Palancı, The new axiomatic characterization of the Shapley value Süleyman Demirel University Faculty of Arts and Science Journal of Science 17 (2) (2022) 522-531.
14. R. Branzei, O. Branzei, S. Z. Alparslan Gök, S. Tijs, Cooperative interval games: A survey, Central European Journal of Operations Research 18 (3) (2010) 397-411.
15. J. C. Harsanyi, A bargaining model for cooperative n-person games, in: A. W. Tucker, R. D. Luce (Eds.), Contributions to the Theory of Games, Vol. IV, Princeton University Press, 1959, Ch. 17, pp. 325-355.
16. R. Branzei, D. Dimitrov, S. Tijs, Models in cooperative game theory, game theory and mathematical methods, Springer, Berlin, 2008.
17. S. Z. Alparslan Gök, O. Branzei, R. Branzei, S. Tijs, Set-valued solution concepts using interval-type payoffs for interval games, Journal of Mathematical Economics 47 (4-5) (2011) 621-626.
18. R. Branzei, S. Tijs, S. Z. Alparslan Gök, How to handle interval solutions for cooperative interval games, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18 (2) (2010) 123-132.
19. S. Tijs, Introduction to game theory, Hindustan Book Agency, Gurgaon, 2003.
20. R. Moore, Methods and applications of interval analysis, SIAM Studies in Applied and Numerical Mathematics, Philadelphia, 1979.
21. A. Casajus, The Shapley value without efficiency and additivity, Mathematical Social Sciences 68 (2014) 1-4.