A Simplified Expression of Share Functions for Cooperative Games with Fuzzy Coalitions

[1] AUBIN, J. P.: Cooperative fuzzy games, Math. Oper. Res. 6 (1988), 1-13.10.1287/moor.6.1.1Search in Google Scholar

[2] AUBIN, J. P.: Mathematical Methods of Game and Economic Theory. (Reprint of the 1982 revised ed.), Dover Publ., Mineola, NY, 2007.Search in Google Scholar

[3] ALVAREZ-MOZOS, M.-VAN DEN BRINK, R.-VAN DER LAAN, G.-TEJADA, O.: Share functions for cooperative games with levels structure of cooperation, European J. Oper. Res. 244 (2013), 167-179.10.1016/j.ejor.2012.07.031Search in Google Scholar

[4] AUMANN, R. J.-SHAPLEY, L. S.: Values of Non-Atomic Games. Princeton Univ. Press, Princeton, NJ, 1974.Search in Google Scholar

[5] AUMANN, R.-HART, S. (EDS.): Handbook of Game Theory with Economic Applications, in: Handbooks in Economics, Vol. 11, Elsevier, Amsterdam, 2002.Search in Google Scholar

[6] BANZHAF, J. F: Weighted voting doesn’t work: a mathematical analysis, Rutgers Law Review 19 (1965), 317-343.Search in Google Scholar

[7] BUTNARIU, D.: Stability and Shapley value for an n-persons fuzzy game, Fuzzy Sets Syst. 4 (1980), 63-72.10.1016/0165-0114(80)90064-0Search in Google Scholar

[8] CHOQUET, G.: Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953), 131-295.10.5802/aif.53Search in Google Scholar

[9] LI, S.-ZHANG, Q.: A simplified expression of the Shapley function for fuzzy game, European J. Oper. Res. 196 (2009), 234-245.10.1016/j.ejor.2008.02.034Search in Google Scholar

[10] MENG, F. Y.-ZHANG, Q.: The Shapley Value on a kind of cooperative fuzzy games, J. Comput. Inform. Syst. 7 (2011), 1846-1854.Search in Google Scholar

[11] MENG, F. Y.-ZHANG, Q.: The Shapley function for fuzzy cooperative games with multilinear extension form, European J. Oper. Res. 23 (2010), 644-650.Search in Google Scholar

[12] SHAPLEY, L. S.: A value for n-person games, Ann. of Math. Stud. 28 (1953), 307-317.Search in Google Scholar

[13] SPRUMONT, Y.: Population monotonic allocation schemes for cooperative games with transferable utility, Games Econom. Behav. 2 (1990), 378-394.10.1016/0899-8256(90)90006-GSearch in Google Scholar

[14] TAN, C.-JIANG, Z. Z.-CHEN, X.-IP, W. H.: A Banzhaf function for fuzzy game, IEEE Trans. Fuzzy Syst. 22 (2014), 1489-1502.10.1109/TFUZZ.2013.2297153Search in Google Scholar

[15] TSURUMI, M.-TANINO, T.-INUIGUCHI, M.: A Shapley function on a class of cooperative fuzzy games, Eur. J. Oper. Res. 129 (2001), 596-618.10.1016/S0377-2217(99)00471-3Search in Google Scholar

[16] VAN DER LAAN, G.-VAN DEN BRINK, R.: Axiomatizations of a class of share functions on n-person games, Theory and Decision 44 (1998), 117-148.10.1023/A:1004972127482Search in Google Scholar

[17] VAN DER LAAN, G.-VAN DEN BRINK, R.: The normalized Banzhaf value and the Banzhaf share function, Int. J. Math. Game Theory Algebra 9 (1999), 65-84.Search in Google Scholar

[18] VAN DER LAAN, G.-VAN DEN BRINK, R.: A class of consistent share functions for games in coalition structure, Games Econom. Behav. 51 (2005), 193-212.10.1016/j.geb.2003.05.004Search in Google Scholar