Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 6
229
Views
3
CrossRef citations to date
0
Altmetric
Articles

The Owen and Banzhaf–Owen values revisited

, , &
Pages 1277-1291 | Received 07 Jan 2015, Accepted 27 Aug 2015, Published online: 07 Oct 2015

References

  • Aumann RJ, Drèze J. Cooperative games with coalition structures. Int. J. Game Theory. 1974;3:217–237.
  • Owen G. Values of games with a priori unions. In: Henn R, Moeschlin O, editors. Mathematical economics and game theory. Berlin: Springer; 1977. p. 76–88.
  • Owen G. Modification of the Banzhaf--Coleman index for games with a priori unions. In: Holler MJ, editor. Power, voting and voting power. Würzburg: Physica-Verlag; 1982. p. 232–238.
  • Vázquez-Brage M, van den Nouweland A, García-Jurado I. Owen’s coalitional value and aircraft landing fees. Math. Soc. Sci. 1997;34:273–286.
  • Hart S, Kurz M. Endogeneous formation of coalitions. Econometrica. 1983;51:1047–1064.
  • Winter E. The consistency and potential for values with coalition structure. Games Econ. Behav. 1992;4:132–144.
  • Hamiache G. A new axiomatization of the Owen value for games with coalition structures. Math. Soc. Sci. 1999;37:281–305.
  • Albizuri MJ. Axiomatizations of Owen value without efficiency. Math. Soc. Sci. 2008;55:78–89.
  • Amer R, Carreras F. Cooperation indices and coalition value. TOP. 1995;3:117–135.
  • Calvo E, Lasaga J, Winter E. The principle of balanced contributions and hierarchies of cooperation. Math. Soc. Sci. 1996;31:171–182.
  • Gómez-Rúa M, Vidal-Puga J. The axiomatic approach to three values in games with coalition structure. European J. Oper. Res. 2010;207:795–806.
  • Gómez-Rúa M, Vidal-Puga J. Balanced per capita contributions and levels structure of cooperation. TOP. 2011;19:167–176.
  • Albizuri MJ. An axiomatization of the modified Banzhaf--Coleman index. Int. J. Game Theory. 2001;30:167–176.
  • Lehrer E. An axiomatization of the Banzhaf value. Int. J. Game Theory. 1988;17:89–99.
  • Amer R, Carreras F, Giménez JM. The modified Banzhaf value for games with coalition structure: an axiomatic characterization. Math. Soc. Sci. 2002;43:45–54.
  • Laruelle A, Valenciano F. On the meaning of Owen-Banzhaf coalitional value in voting situations. Theory Decis. 2004;56:113–123.
  • Alonso-Meijide JM, Carreras F, Fiestras-Janeiro MG, et al. A comparative axiomatic characterization of the Banzhaf-Owen coalitional value. Decis. Support Syst. 2007;43:701–712.
  • van den Brink R, van der Laan G. A class of consistent share functions for games in coalition structure. Games Econ. Behav. 2005;51:193–212.
  • Shapley LS. A value for n-person games. In: Kuhn HW, Tucker AW, editors. Contributions to the theory of games II. Princeton, NJ: Princeton University Press; 1953. p. 307–317.
  • Banzhaf JF. Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev. 1965;19:317–343.
  • Nowak AS. On an axiomatization of the Banzhaf value without the additivity axiom. Int. J. Game Theory. 1997;26:137–141.
  • Alonso-Meijide JM, Casas-Méndez B, González-Rueda A, et al. Axiomatic of the Shapley value of a game with a priori unions. TOP. 2014;22:749–770.
  • Myerson RB. Conference structures and fair allocation rules. Int. J. Game Theory. 1980;9:169–182.
  • Alonso-Meijide JM, Carreras F, Puente MA. Axiomatic characterizations of the symmetric coalitional binomial semivalues. Discrete Appl. Math. 2007;155:2282–2293.
  • Álvarez-Mozos M, Tejada O. Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with levels structure of cooperation. Decis. Support Syst. 2011;52:21–27.
  • Lorenzo-Freire S, Alonso-Meijide JM, Casas-Méndez B, et al. Balanced contributions for TU games with awards and applications. Eur. J. Oper. Res. 2007;182:958–964.
  • Alonso-Meijide JM, Fiestras-Janeiro MG. Modification of the Banzhaf value for games with a coalition structure. Ann. Oper. Res. 2002;109:213–227.
  • Lorenzo-Freire S. New characterizations of the Owen and the Banzhaf-Owen value using the intracoalitional balanced contributions property. Spain: MODES Research Group, Department of Mathematics, University of A Coruña; 2015. Available from: http://dm.udc.es/modes/sites/default/files/owen\_banzhaf1.pdf.
  • Vidal-Puga J. The Harsanyi paradox and the ‘right to talk’ in bargaining among coalitions. Math. Soc. Sci. 2012;64:214–224.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.