Abstract
We investigate under what conditions equal treatment property and symmetry of a value for cooperative games are equivalent. For additive values, null player property or efficiency is sufficient for the equivalence. When additivity is replaced by fairness, both equivalences cease to be true. But the marginal contributions condition ensures the equivalence without any additional assumptions.
M. Malawski—I am grateful to two anonymous referees for their helpful remarks and for correcting some minor errors in the paper. Any remaining errors are, of course, my own.
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Notes
- 1.
For multivalued solutions an alternative stronger version of equal treatment is discussed by Aumann [2].
- 2.
Weber actually assumes symmetry instead of equal treatment, but theorem 1 ensures that the two are equivalent.
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Malawski, M. (2020). A Note on Equal Treatment and Symmetry of Values. In: Nguyen, N.T., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXV. Lecture Notes in Computer Science(), vol 12330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-62245-2_5
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