The Banzhaf value for generalized probabilistic communication situations

• Alonso-Meijide, J. M., Carreras, F., Fiestras-Janeiro, M. G., & Owen, G. (2007). A comparative axiomatic characterization of the Banzhaf–Owen coalitional value. Decision Support Systems, 43, 701–712.

  Article  Google Scholar 

• Alonso-Meijide, J. M., & Fiestras-Janeiro, M. G. (2002). Modification of the Banzhaf value for games with a coalition structure. Annals of Operations Research, 109, 213–227.

  Article  Google Scholar 

• Alonso-Meijide, J. M., & Fiestras-Janeiro, M. G. (2006). The Banzhaf value and communication situations. Naval Research Logistics, 53(3), 198–203.

  Article  Google Scholar 

• Amer, R., Carreras, F., & Giménez, J. M. (2002). The modified Banzhaf value for games with coalition structure: An axiomatic characterization. Mathematical Social Sciences, 43, 45–54.

  Article  Google Scholar 

• Banzhaf, J. F. (1965). Weighted voting does not work: A mathematical analysis. Rutgers Law Review, 19, 317–343.

  Google Scholar 

• Calvo, E., Lasaga, J., & van den Nouweland, A. (1999). Values of games with probabilistic graphs. Mathematical Social Sciences, 37, 79–95.

  Article  Google Scholar 

• Casajus, A. (2011). Marginality, differential marginality, and the Banzhaf value. Theory and Decision, 71, 365–372.

  Article  Google Scholar 

• Dragan, I. (1996). New mathematical properties of the Banzhaf value. European Journal of Operational Research, 95(2), 451–463.

  Article  Google Scholar 

• Feltkamp, V. (1995). Alternative axiomatic characterization of the Shapley and Banzhaf values. International Journal of Game Theory, 24, 179–186.

  Article  Google Scholar 

• Ghintran, A., González-Arangüena, E., & Manuel, C. (2012). A probabilistic position value. Annals of Operations Research, 1, 183–196.

  Article  Google Scholar 

• Gómez, D., González-Arangüena, E., Manuel, C., & Owen, G. (2008). A value for generalized probabilistic communication situations. European Journal of Operational Research, 190, 539–556.

  Article  Google Scholar 

• Haimanko, O. (2019). Composition independence in compound games: A characterization of the Banzhaf power index and the Banzhaf value. International Journal of Game Theory, 48, 755–768.

  Article  Google Scholar 

• Harsanyi, J. C. (1959). A bargaining model for cooperative \(n\)-person games. In A. W. Tucker & R. D. Luce (Eds.), Contributions to the theory of games IV (pp. 325–355). Princeton, NJ: Princeton University Press.

  Google Scholar 

• Meessen, R. (1988). Communication games, Master’s thesis, Department of Mathematics, University of Nijmegen, The Netherlands (in Dutch).

• Myerson, R. B. (1977). Graphs and cooperation in games. Mathematics of Operations Research, 2(3), 225–229.

  Article  Google Scholar 

• Owen, G. (1975). Multilinear extensions and the Banzhaf value. Naval Research Logistics, 22, 741–750.

  Article  Google Scholar 

• Owen, G. (1986). Values of graph-restricted games. SIAM Journal on Discrete Mathematics, 7, 210–220.

  Article  Google Scholar 

• Ridaoui, M., Grabisch, M., & Labreuche, C. (2018). An axiomatization of the Banzhaf value and interaction index for multichoice games. Université Panthéon-Sorbonne (Paris 1), Centre d’Economie de la Sorbonne.

• Shapley, L. S. (1953). A value for \(n\)-person games. In H. Kuhn & A. Tucker (Eds.), Contributions to the theory of games II (pp. 307–317). Princeton: Princeton University Press.

  Google Scholar 

• Slikker, M. (2005). Link monotonic allocation schemes. International Game Theory Review, 7, 473–489.

  Article  Google Scholar 

• Slikker, M., van den Nouweland, A. (2001). Social and economic networks in cooperative game theory. In Theory and Decision Library (Vol. 27).

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