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The D&P Shapley Value: a Weighted Extension

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Ukrainian Mathematical Journal Aims and scope

First, we propose a weighted extension of the D&P Shapley value and then study several equivalences between the potentializability and other properties. On the basis of these equivalences and consistency, we also propose two axiomatizations.

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References

  1. E. Calvo and J. C. Santos, “Potential in cooperative TU-games,” Math. Soc. Sci., 34, 175–190 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Derks and H. Peters, “A Shapley value for games with restricted coalitions,” Int. J. Game Theory, 21, 351–360 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Hart and A. Mas-Colell, “Potential, value and consistency,” Econometrica, 57, 589–614 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. A. Hwang and Y. H. Liao, “Potential approach and characterizations of a Shapley value in multichoice games,” Math. Soc. Sci., 56, 321–335 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Klijn, M. Slikker, and J. Zazuelo, “Characterizations of a multichoice value,” Int. J. Game Theory, 28, 521–532 (1999).

    Article  MATH  Google Scholar 

  6. K. M. Ortmann, “Preservation of differences, potential, conservity,” Working Paper, Univ. Bielefeld, No. 236 (1995).

  7. K. M. Ortmann, “Conservation of energy in nonatomic games,” Working Paper, Univ. Bielefeld, No. 237 (1995).

  8. L. S. Shapley, “A value for n-person game,” Ann. Math. Stud., Princeton Univ. Press, Princeton, 28, 307–317 (1953).

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 1, pp. 131–141, January, 2016.

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Liao, YH. The D&P Shapley Value: a Weighted Extension. Ukr Math J 68, 144–157 (2016). https://doi.org/10.1007/s11253-016-1214-5

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  • DOI: https://doi.org/10.1007/s11253-016-1214-5

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