Cooperation Tendencies and Evaluation of Games

Francesc Carreras, María Albina Puente

2013

Abstract

Multinomial probabilistic values were first introduced by one of us in reliability and later on by the other, independently, as power indices. Here we study them on cooperative games from several viewpoints, and especially as a powerful generalization of binomial semivalues. We establish a dimensional comparison between multinomial values and binomial semivalues and provide two characterizations within the class of probabilistic values: one for each multinomial value and another for the whole family. An example illustrates their use in practice as power indices.

References

  1. Alonso, J. M., Carreras, F. and Puente, M. A. (2007): “Axiomatic characterizations of the symmetric coalitional binomial semivalues.” Discrete Applied Mathematics 155, 2282-2293.
  2. Carreras, F. (2004): “a-decisiveness in simple games.” Theory and Decision 56, 77-91. Also in: Essays on Cooperative Games (G. Gambarelli, ed.), Kluwer Academic Publishers, 77-91.
  3. Carreras, F. and Puente, M. A. (2012): “Symmetric coalitional binomial semivalues.” Group Decision and Negotiation 21, 637-662.
  4. Dubey, P., Neyman, A. and Weber, R. J. (1981): “Value theory without efficiency.” Mathematics of Operations Research 6, 122-128.
  5. Feltkamp, V. (1995): “Alternative axiomatic characterizations of the Shapley and Banzhaf values.” International Journal of Game Theory 24, 179-186.
  6. Freixas, J. and Puente, M. A. (2002): “Reliability importance measures of the components in a system based on semivalues and probabilistic values.” Annals of Operations Research 109, 331-342.
  7. Owen, G. (1972): “Multilinear extensions of games.” Management Science 18, 64-79.
  8. Owen, G. (1975): “Multilinear extensions and the Banzhaf value.” Naval Research Logistics Quarterly 22, 741- 750.
  9. Shapley, L. S. (1953): “A value for n-person games.” In: Contributions to the Theory of Games II (H.W. Kuhn and A.W. Tucker, eds.), Princeton University Press, Annals of Mathematical Studies 28, 307-317.
  10. Weber, R. J. (1988): “Probabilistic values for games.” In: The Shapley Value: Essays in Honor of Lloyd S. Shapley (A.E. Roth, ed.), Cambridge University Press, 101-119.
Download


Paper Citation


in Harvard Style

Carreras F. and Puente M. (2013). Cooperation Tendencies and Evaluation of Games . In Proceedings of the 15th International Conference on Enterprise Information Systems - Volume 1: ICEIS, ISBN 978-989-8565-59-4, pages 415-422. DOI: 10.5220/0004414104150422


in Bibtex Style

@conference{iceis13,
author={Francesc Carreras and María Albina Puente},
title={Cooperation Tendencies and Evaluation of Games},
booktitle={Proceedings of the 15th International Conference on Enterprise Information Systems - Volume 1: ICEIS,},
year={2013},
pages={415-422},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004414104150422},
isbn={978-989-8565-59-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 15th International Conference on Enterprise Information Systems - Volume 1: ICEIS,
TI - Cooperation Tendencies and Evaluation of Games
SN - 978-989-8565-59-4
AU - Carreras F.
AU - Puente M.
PY - 2013
SP - 415
EP - 422
DO - 10.5220/0004414104150422