Abstract
The principle of differential marginality (Casajus in Theory and Decis 71(2):163-–174) for cooperative games is a very appealing property that requires equal productivity differentials to translate into equal payoff differentials. In this paper we apply this property to axiomatic characterizations of values. We show that differential marginality implies additivity and symmetry under certain conditions. Based on this result, we propose new characterizations of the equal division and the equal surplus division values. Finally, we characterize two classes of convex combinations of values, i.e., \(\alpha\)-egalitarian Shapley values and \(\alpha\)-equal surplus division values, by employing differential marginality and establishing the uniqueness of these values on inessential games.
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Notes
In Theorem 1 of Aczél and Oser (1966), they showed that f is linear if f is additive and monotonic.
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Acknowledgements
We are grateful to the reviewers for carefully reading and the invaluable comments and suggestions, which improves the presentation greatly. This research was partially supported by the National Nature Science Foundation of China (No. 72371151).
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Cui, Z., Shan, E. & Lyu, W. Differential marginality, inessential games and convex combinations of values. Theory Decis 96, 463–475 (2024). https://doi.org/10.1007/s11238-023-09954-8
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DOI: https://doi.org/10.1007/s11238-023-09954-8