SHAN Er-fang, LI Kang, LIU Zhen. The Weighted Position Value with the Hypergraph Cooperation Structure[J]. Operations Research and Management Science, 2019, 28(6): 109-117.
[1] Branzei R, Dimitrov D, Tijs S. Models in cooperative game theory[M]. Berlin: Springer, 2008. [2] Myerson R B. Graphs and cooperation in games[J]. Mathematics of Operations Research, 1977, 2(3): 225-229. [3] Borm P, Owen G, Tijs S. On the position value for communication situations[J]. Society for Industrial and Applied Mathematics , 1992, 5(3): 305-320. [4] Myerson R B. Conference structures and fair allocation rules[J]. International Journal of Game Theory, 1980, 9(3): 169-182. [5] van den Nouweland A, Borm P, Tijs S. Allocation rules for hypergraph communication situations[J]. International Journal of Game Theory, 1992, 20(3): 255-268. [6] Meessen R. Communication games[J]. Master’s thesis, Department of Mathematics, University of Nijmegen, The Netherlands, 1988. [7] Shapley L S. A value for n-person games[J]. Contributions to the Theory of Games, 1953, 2(28): 307-317. [8] Shapley L S. Additive and non-additive set functions[M]. Princeton University, 1953. [9] Owen G. A note on the Shapley value[J]. Management Science, 1968, 14(11): 731-731. [10] Kalai E, Samet D. On weighted Shapley values[J]. International Journal of Game Theory, 1987, 16(3): 205-222. [11] Chun Y. On the symmetric and weighted Shapley values[J]. International Journal of Game Theory, 1991, 20(2): 183-190. [12] Haeringer G. A new weight scheme for the shapley value[J]. Mathematical Social Sciences, 2006, 52(1): 88-98. [13] Haeringer G. Weighted myerson value[J]. International Game Theory Review, 1999, 1(02): 187-192. [14] Slikker M, van den Nouweland A. Communication situations with asymmetric players[J]. Mathematical Methods of Operations Research, 2000, 52(1): 39-56. [15] van den Brink R, van der Laan G, Pruzhansky V. Harsanyi power solutions for graph-restricted games[J]. International Journal of Game Theory, 2011, 40(1): 87-110.