On the comparison of Shapley values for variance and standard deviation games
Motivated by the problem of variance allocation for the sum of dependent random variables, Colini-Baldeschi, Scarsini and Vaccari (2018) recently introduced Shapley values for variance and standard deviation games. These Shapley values constitute a criterion satisfying nice properties useful for all...
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| Veröffentlicht in: | Journal of applied probability 2021-09, Vol.58 (3), p.609-620 |
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| container_title | Journal of applied probability |
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| creator | Galeotti, Marcello Rabitti, Giovanni |
| description | Motivated by the problem of variance allocation for the sum of dependent random variables, Colini-Baldeschi, Scarsini and Vaccari (2018) recently introduced Shapley values for variance and standard deviation games. These Shapley values constitute a criterion satisfying nice properties useful for allocating the variance and the standard deviation of the sum of dependent random variables. However, since Shapley values are in general computationally demanding, Colini-Baldeschi, Scarsini and Vaccari also formulated a conjecture about the relation of the Shapley values of two games, which they proved for the case of two dependent random variables. In this work we prove that their conjecture holds true in the case of an arbitrary number of independent random variables but, at the same time, we provide counterexamples to the conjecture for the case of three dependent random variables. |
| doi_str_mv | 10.1017/jpr.2020.106 |
| format | Article |
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| source | Cambridge University Press Journals Complete |
| subjects | Dependent variables Game theory Games Independent variables Inequality Original Article Queuing theory Random variables Research Papers Standard deviation Variance |
| title | On the comparison of Shapley values for variance and standard deviation games |
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