Game Solutions, Probability Transformations and the Core

Enrique Miranda; Ignacio Montes

Game Solutions, Probability Transformations and the Core

Enrique Miranda, Ignacio Montes

Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:217-228, 2017.

Abstract

We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations of lower probabilities. The first one coincides with the pignistic transformation proposed in the Transferable Belief Model the second one is not efficient in general, leading us to propose a normalized version. We consider a number of particular cases of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distorsion models. For them, we provide some alternative expressions of the transformations and study when they belong to the core of the lower probability.

Cite this Paper

BibTeX


@InProceedings{pmlr-v62-miranda17a,
  title = 	 {Game Solutions, Probability Transformations and the Core},
  author = 	 {Miranda, Enrique and Montes, Ignacio},
  booktitle = 	 {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications},
  pages = 	 {217--228},
  year = 	 {2017},
  editor = 	 {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien},
  volume = 	 {62},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {10--14 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v62/miranda17a/miranda17a.pdf},
  url = 	 {https://proceedings.mlr.press/v62/miranda17a.html},
  abstract = 	 {We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations of lower probabilities. The first one coincides with the pignistic transformation proposed in the Transferable Belief Model the second one is not efficient in general, leading us to propose a normalized version. We consider a number of particular cases of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distorsion models. For them, we provide some alternative expressions of the transformations and study when they belong to the core of the lower probability.}
}

Endnote

%0 Conference Paper
%T Game Solutions, Probability Transformations and the Core
%A Enrique Miranda
%A Ignacio Montes
%B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications
%C Proceedings of Machine Learning Research
%D 2017
%E Alessandro Antonucci
%E Giorgio Corani
%E Inés Couso
%E Sébastien Destercke	
%F pmlr-v62-miranda17a
%I PMLR
%P 217--228
%U https://proceedings.mlr.press/v62/miranda17a.html
%V 62
%X We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations of lower probabilities. The first one coincides with the pignistic transformation proposed in the Transferable Belief Model the second one is not efficient in general, leading us to propose a normalized version. We consider a number of particular cases of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distorsion models. For them, we provide some alternative expressions of the transformations and study when they belong to the core of the lower probability.

APA


Miranda, E. & Montes, I.. (2017). Game Solutions, Probability Transformations and the Core. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:217-228 Available from https://proceedings.mlr.press/v62/miranda17a.html.

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